Hebrews writes of believers as entering in to their own rest saying," he also hath ceased from his own works, as God did from his. (Heb 4:10) What are 'my own works'?
You kind of answered your own question within the question. Not sure if that was deliberate on your part. “Your own works” are the works of the flesh. Those strivings, efforts and struggles to achieve righteousness through the keeping of the Law. That stands in contra distinction to imputed righteousness received by faith
If one were to consider the LXX and where the word for rest is found in the LXX that corresponds with Hebrews 4:10 passage, one would come across these four references
“for as yet you have not come to the rest and the inheritance which the LORD your God is giving you.” Deuteronomy 12:9
Take note of the word rest, but also inheritance, which is unearned but received by one qualified from another who has it to give.
““Blessed be the LORD, who has given rest to His people Israel, according to all that He promised. There has not failed one word of all His good promise, which He promised through His servant Moses.” I Kings 8:56
Despite this rest being achieved in the natural it wouldn’t last. This isn’t the rest that the writer of Hebrews allures to that existed from Creation.
““Now therefore, Arise, O LORD God, to Your resting place, You and the ark of Your strength. Let Your priests, O LORD God, be clothed with salvation, And let Your saints rejoice in goodness.” II Chronicles 6:41
Solomon’s dedication of the temple prayer, is asking God to rest, but rather it is man that should be resting in God and taking his place in God(Jesus or IN HIM).
“So I swore in My wrath, ‘They shall not enter My rest.’ ”” Psalms 95:11
There are dual fulfillment prophecies, near and distant. It would appear that yes the generation that was favored by God to be taken out of Egypt preferred to go to war with the Canaanites in their own strength rather than trust God. And because they lacked faith in God they did not enter the promised land. But the author of Hebrew uses this verse to make the point that they lacked faith
“For indeed the gospel was preached to us as well as to them; but the word which they heard did not profit them, not being mixed with faith in those who heard it. For we who have believed do enter that rest, as He has said: “So I swore in My wrath, ‘They shall not enter My rest,’ ” although the works were finished from the foundation of the world.” Hebrews 4:2-3
The work was finished from the foundation of the world is also pertinent because that is where the rest truly lies, IN HIM.
“just as He chose us in Him before the foundation of the world, that we should be holy and without blame before Him in love, having predestined us to adoption as sons by Jesus Christ to Himself, according to the good pleasure of His will, to the praise of the glory of His grace, by which He made us accepted in the Beloved.” Ephesians 1:4-6
This rest was predestined and predetermined IN Christ before the foundation of the world. We were not present IN HIM but it was prepared for whosoever should Believe IN HIM, would enter into that which was prepared prior to Creation in anticipation of a rest to come. Now only those who by faith enter in, voluntarily, of their own according, they alone enter into the rest found IN HIM.
“What shall we say then? That Gentiles, who did not pursue righteousness, have attained to righteousness, even the righteousness of faith; but Israel, pursuing the law of righteousness, has not attained to the law of righteousness. Why? Because they did not seek it by faith, but as it were, by the works of the law. For they stumbled at that stumbling stone.” Romans 9:30-32
Notice it’s the gospel that was preached to all but only by faith can rest be attained.
So the striving after the Law in an attempt to attain personal righteousness by way of the flesh is a futile endeavor because it’s endless and there is no rest with fulfilling the Law.
But those who by faith accept to enter into the REST that is IN HIM, that is, in Christ Jesus, they receive the imputed righteousness and inherit all things that come with being IN HIM.
“He who did not spare His own Son, but delivered Him up for us all, how shall He not with Him also freely give us all things?” Romans 8:32
But of course God anticipated that ALL should come to the knowledge of salvation/truth but unfortunately the gate is narrow and the way hard, few find it.
“For this is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth. For there is one God and one Mediator between God and men, the Man Christ Jesus, who gave Himself a ransom for all, to be testified in due time,” I Timothy 2:3-6
The rest offered is found only IN CHRIST, one can only enter into this rest by ceasing to work their way into LIFE by means of self righteous acts which are filthy rags in God’s sight.
Righteousness that is acceptable is HIS righteousness Matthew 6:33, this is imputed freely, and by faith. Grace comes by way of faith and not vice versa, where there is no faith there is no grace.
“For by grace you have been saved through faith, and that not of yourselves; it is the gift of God,” Ephesians 2:8
It’s free, salvation that is, is free, if you receive it by faith. You can’t boast about a salvation you received for free. (Faith is not the gift, it’s salvation that is the gift).