The covenant / promise of the rainbow even today reminds us of God's promise to Noah. In Gen. 8:21-22 God stated that he would never again curse the earth for man's sake. In Gen. chap. 9 He told Noah that never again would the rains cover the entire earth. The rainbow was the sign from God to man that He would never again bring a world-wide destruction upon the earth.
In prophesy, God used the word "flood" as a metaphor for a destroying army.
"Behold, the Lord hath a mighty and strong one, which as a tempest of hail and a destroying storm, as a flood of mighty waters overflowing, shall cast down to the earth with the hand." (KJV)
"So shall they fear the name of the Lord from the west, and his glory from the rising of the sun. When the enemy shall come in like a flood, the Spirit of the Lord shall lift up a standard against him."
"Egypt riseth up like a flood, and his waters are moved like the rivers; and he saith, I will go up, and will cover the earth; I will destroy the city and the inhabitants thereof."
Whenever God is sitting on His throne, He is sitting in judgment. A king will sit on his throne to hear reports from his council, and listen to requests from the people. The king dispenses judgment from the throne, answering the council and people. The king will also announce rules and laws from the throne.
"But the Lord shall endure for ever: he hath prepared his throne for judgment."
"Justice and judgment are the habitation of thy throne: mercy and truth shall go before thy face."
The sign of the rainbow around the throne of judgment was a comfort to the prophet and the people, that His judgment was tempered with mercy. The destruction foretold would not be a world-wide destruction, only a limited one upon the wicked who had rebelled against Him. The rainbow meant that a remnant would be saved.
In Ezekiel the judgment was for the still coming destruction of Jerusalem and the temple. While many of Judah had been taken captive into Babylon, the city and the temple had not yet been destroyed.
Excerpt from Keil and Delitzsch Biblical Commentary on Ezek. 4:1:
"The meaning is not, that upon the roll was inscribed a multitude of mournful expressions of every kind, but that there was written upon it all that the prophet was to announce, and what we now read in his book. These contents were of a mournful nature, for they related to the destruction of the kingdom, the destruction of Jerusalem and of the temple." Source: Biblehub
Just as in Ezekiel, Revelation was again the prophesy of the complete destruction of the city and the temple of Jerusalem.
Excerpt again from Keil and Delitzsch on Ezek. 5:8,
"The punishment to be suspended shall be so great and heavy, that the like has never happened before, nor will ever happen again. These words do not require us either to refer the threatening, with Coccejus, to the last destruction of Jerusalem, which was marked by greater severity than the earlier one, or to suppose, with Hvernick, that the prophet's look is directed to both the periods of Israel's punishment - the times of the Babylonian and Roman calamity together. Both suppositions are irreconcilable with the words, as these can only be referred to the first impending penal judgment of the destruction of Jerusalem. This was, so far, more severe than any previous or subsequent one, inasmuch as by it the existence of the people of God was for a time suspended, while that Jerusalem and Israel, which were destroyed and annihilated by the Romans, were no longer the people of God, inasmuch as the latter consisted at that time of the Christian community, which was not affected by that catastrophe (Kliefoth)." Source: Biblehub
The rainbow is also seen around the strong messenger (YLT), the mighty angel of Rev. 10:1,
"And I saw another mighty angel come down from heaven, clothed with a cloud: and a rainbow was upon his head, and his face was as it were the sun, and his feet as pillars of fire:"
The strong messenger was Christ, with one foot upon the earth (the land of Judea) and one foot on the sea (the other nations) who told John he would prophesy again, and instructed him in chap. 11 to measure the temple that was about to be destroyed.
The rainbow signified that God would save a remnant of those who believed in Him.
"Yet will I leave a remnant, that ye may have some that shall escape the sword among the nations, when ye shall be scattered through the countries."
In the first destruction of the city, God would bring back about 50,000 to rebuild Jerusalem and the temple, to restore the people to a covenant relationship with God. (Ezra 2:1-2; Hag. 1:1)
In the second destruction under the Roman empire in AD 70, the remnant of believers were the Jews who had followed Christ, who survived by fleeing from Jerusalem (Matt. 24: 15-20). They were dispersed into all the world, and the remnant who were baptized into Christ continued to spread the gospel through each generation of those will will believe.
I have more on "The Signs of Revelation" at my blog ShreddingTheVeil in Parts I - VIII. Part IV discusses the symbols of the throne scene.
(All scripture is from the KJV. All bold emphasis is mine.)