The audience to whom the writer of "Hebrews" is indicated in every extant manuscript as "To the Hebrews". It is written to the new covenant Jews ("the Israel of God") to explain how the new covenant works. (To read this scroll as if it were about Catholics, Protestant or Jehovah's Witnesses is part a lack of circumspect and part hubris).
The setting is 1st century Jerusalem. The Messiah had died to ratify the new covenant with God's people (IE: the elect of the houses of Israel and Judah). He has received the promise of the spirit and poured it all over Jerusalem so that a huge revival breaks out:
[Mat 3:5-6 NKJV] 5 Then Jerusalem, all Judea, and all the region around the Jordan went out to him 6 and were baptized by him in the Jordan, confessing their sins.
It was the signal of the beginning of the Messianic age:
[Zec 13:1 KJV] 1 In that day there shall be a fountain opened to the house of David and to the inhabitants of Jerusalem for sin and for uncleanness.
[Mal 4:5 KJV] 5 Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the LORD:
Jesus said that the sign of the beginning of the Messianic age had already arrived:
[Mat 17:12 NKJV] 12 "But I say to you that Elijah has come already, and they did not know him but did to him whatever they wished. Likewise the Son of Man is also about to suffer at their hands."
Another sign was the pouring out of the spirit on all flesh upon Jerusalem, which is referred to as "the Promise of the Father" and again Peter says that this sign has arrived as well:
[Act 2:16-21 KJV] 16 But this is that which was spoken by the prophet Joel; 17 And it shall come to pass in the last days, saith God, I will pour out of my Spirit upon all flesh: and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams: 18 And on my servants and on my handmaidens I will pour out in those days of my Spirit; and they shall prophesy: 19 And I will shew wonders in heaven above, and signs in the earth beneath; blood, and fire, and vapour of smoke: 20 The sun shall be turned into darkness, and the moon into blood, before that great and notable day of the Lord come: 21 And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved.
In fact, Peter boldly proclaims that every prophecy would be fulfilled in "these days":
[Act 3:24 KJV] 24 Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days.
By saying "these days" Peter is alluding to Zechariah 8:15:
[Zec 8:7-15 KJV] 7 Thus saith the LORD of hosts; Behold, I will save my people from the east country, and from the west country; 8 And I will bring them, and they shall dwell in the midst of Jerusalem: and they shall be my people, and I will be their God, in truth and in righteousness. 9 Thus saith the LORD of hosts; Let your hands be strong, ye that hear in these days these words by the mouth of the prophets, which were in the day that the foundation of the house of the LORD of hosts was laid, that the temple might be built. 10 For before these days there was no hire for man, nor any hire for beast; neither was there any peace to him that went out or came in because of the affliction: for I set all men every one against his neighbour. 11 But now I will not be unto the residue of this people as in the former days, saith the LORD of hosts. 12 For the seed shall be prosperous; the vine shall give her fruit, and the ground shall give her increase, and the heavens shall give their dew; and I will cause the remnant of this people to possess all these things. 13 And it shall come to pass, that as ye were a curse among the heathen, O house of Judah, and house of Israel; so will I save you, and ye shall be a blessing: fear not, but let your hands be strong. 14 For thus saith the LORD of hosts; As I thought to punish you, when your fathers provoked me to wrath, saith the LORD of hosts, and I repented not: 15 So again have I thought in these days [IE: the "day" of the LORD] to do well unto Jerusalem and to the house of Judah: fear ye not.
Notice that it is the day of the "Seed" and the "Vine", both Messianic titles. These are not promises for our day but rather for the "Hebrews" of the first century - the Messianic age/millennium.
So what "To the Hebrews" is alluding to:
[Jdg 5:31 KJV] 31 So let all thine enemies perish, O LORD: but let them that love him be as the sun when he goeth forth in his might. And the land had rest forty years.
The passage speaks of a day when all of God's enemies (in this case, the apostate Jews that persecute his elect remnant) are destroyed while his elect remnant are transformed into a radiant "city on a hill":
[Mat 5:14-16 KJV] 14 Ye [IE: like the sun] are the light of the world. A city that is set on an hill cannot be hid. 15 Neither do men light a candle, and put it under a bushel, but on a candlestick; and it giveth light unto all that are in the house. 16 Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven.
This is the new Jerusalem, not the old earthly Jerusalem:
[Rev 21:23 ASV] 23 And the city hath no need of the sun, neither of the moon, to shine upon it: for the glory of God did lighten it, and the lamp thereof is the Lamb.
[Gal 4:25-31 ASV] 25 Now this Hagar is mount Sinai in Arabia and answereth [IE: "corresponds"] to the Jerusalem that now is: for she is in bondage with her children. 26 But the Jerusalem that is above is free, which is our mother. 27 For it is written, Rejoice, thou barren that bearest not; Break forth and cry, thou that travailest not: For more are the children of the desolate than of her that hath the husband. 28 Now we, brethren, as Isaac was, are children of promise. 29 But as then he that was born after the flesh persecuted him that was born after the Spirit, so also it is now. 30 Howbeit what saith the scripture? Cast out the handmaid and her son: for the son of the handmaid shall not inherit with the son of the freewoman. 31 Wherefore, brethren, we are not children of a handmaid, but of the freewoman.
This new covenant People, the Israel of God, is the new Jerusalem:
[Rev 21:1-7 ASV] 1 And I saw a new heaven and a new earth: for the first heaven and the first earth are passed away; and the sea is no more. 2 And I saw the holy city, new Jerusalem, coming down out of heaven from God, made ready as a bride adorned for her husband. 3 And I heard a great voice out of the throne saying, Behold, the tabernacle of God is with men, and he shall dwell with them, and they shall be his peoples, and God himself shall be with them, and be their God: 4 and he shall wipe away every tear from their eyes; and death shall be no more; neither shall there be mourning, nor crying, nor pain, any more: the first things are passed away. 5 And he that sitteth on the throne said, Behold, I make all things new. And he saith, Write: for these words are faithful and true. 6 And he said unto me, They are come to pass. I am the Alpha and the Omega, the beginning and the end. I will give unto him that is athirst of the fountain of the water of life freely. 7 He that overcometh shall inherit these things; and I will be his God, and he shall be my son.
So what "To the Hebrews" is saying is that the forty years of rest mentioned in Joshua 11 and 23 was NOT the same rest as the one promised here, since this rest was promised after Joshua's conquest:
[The rest that Joshua gave]:
[Jos 11:23 ASV] 23 So Joshua took the whole land, according to all that Jehovah spake unto Moses; and Joshua gave it for an inheritance unto Israel according to their divisions by their tribes. And the land had rest from war.
[Jos 23:1 ASV] 1 And it came to pass after many days, when Jehovah had given rest unto Israel from all their enemies round about, and Joshua was old and well stricken in years;
[The later denial of rest to the apostate Jews]:
[Psa 95:11 NLT] 11 So in my anger I took an oath: 'They will never enter my place of rest.'"
[Heb 3:11 NLT] 11 So in my anger I took an oath: 'They will never enter my place of rest.'"
[God's future (to his audience) sabbath rest]:
[Heb 4:3, 5 NLT] 3 For only we who believe can enter his rest. As for the others, God said, "In my anger I took an oath: 'They will never enter my place of rest,'"even though this rest has been ready since he made the world. ... 5 But in the other passage God said, "They will never enter my place of rest."
[Heb 4:8 ASV] 8 For if Joshua had given them rest, he would not have spoken afterward of another day.
The coming rest was the end of all the prophets:
[Dan 9:24 KJV] 24 Seventy weeks are determined upon thy people and upon thy holy city, to finish the transgression, and to make an end of sins, and to make reconciliation for iniquity, and to bring in everlasting righteousness, and to seal up the vision and prophecy, and to anoint the most Holy.
The words "seal up the vision and prophecy" mean that every vision and prophecy would be accomplished, and then the end would come:
חָתַם châtham, khaw-tham'; a primitive root; to close up; especially to seal:—make an end, mark, seal (up), stop.
Since the word in the Hiphel it does not mean "seal up" but rather "make an end":
to seal, seal up, affix a seal
to seal, affix one's seal
to seal up, fasten up by sealing
(Niphal) to seal
(Piel) to lock up
(Hiphil) to be stopped
From "Outline of Biblical Usage"
This is "the end" to which Paul referred:
[1Co 15:24 KJV] 24 Then cometh the end, when he shall have delivered up the kingdom to God, even the Father; when he shall have put down all rule and all authority and power.
The nature of the "rest" for the Hebrew new covenant Jews, though, is that it comes through the martyrdom of the 144,000!:
[Rev 6:11 KJV] 11 And white robes were given unto every one of them; and it was said unto them, that they should rest yet for a little season, until their fellowservants also and their brethren, that should be killed as they were, should be fulfilled.
[Rev 14:13 KJV] 13 And I heard a voice from heaven saying unto me, Write, Blessed are the dead which die in the Lord from henceforth: Yea, saith the Spirit, that they may rest from their labours; and their works do follow them.
For the non-Jewish saints, the rest is not through martyrdom but rather through vengeance on God's enemies at Christ's return:
[2Th 1:4-10 KJV] 4 So that we ourselves glory in you in the churches of God for your patience and faith in all your persecutions and tribulations that ye endure: 5 Which is a manifest token of the righteous judgment of God, that ye may be counted worthy of the kingdom of God, for which ye also suffer: 6 Seeing it is a righteous thing with God to recompense tribulation to them that trouble you; 7 And to you who are troubled rest with us, when the Lord Jesus shall be revealed from heaven with his mighty angels, 8 In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ: 9 Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power; 10 When he shall come to be glorified in his saints, and to be admired in all them that believe (because our testimony among you was believed ) in that day.
The "rest" mentioned in Matthew 11:28 does not appear to me to be a direct reference to the eschatological rest but rather to relief from the mistreatment by the wicked "hireling" shepherds:
[Mat 23:4 KJV] 4 For they bind heavy burdens and grievous to be borne, and lay them on men's shoulders; but they themselves will not move them with one of their fingers.
For more insight, please see this excellent video.