Why will God release Satan after he is bound in the bottomless pit for 1,000 years? To test people?
There a nine ages given in scriptures. Number one isn't really an age, it simply marks the beginning of creation.
1. The Beginning - The Godhead (Father, Son, Holy Spirit) takes possession of the body of the man, Jesus who is designated as Christ through whom God creates all things.
2. The Angelic age - Prior to the physical creation of the universe
3. The age of innocence – Garden of Eden paradise
4. The age of humanism, rule of conscience – After the Garden of Eden before the flood
5. The age of human government – Post flood – from the Ark to a tomb in Egypt
6. The age of Law – From Moses to the Cross
7. The Church age – From the resurrection to the rapture
8. The Satanic age (7-year tribulation where the devil is allowed almost entirely free reign and a man to possess fully) – From the rapture to the second coming (note that this also commences what the Bible calls "the Day of the Lord".)
9. The Kingdom age (Millennium) – From the second coming through 1,000 years (this concludes the Day of the Lord continued)
10. The age of Eternity – From the end of Millennium to infinity (time ceases as we know it)
What you are making reference to is the 9th age, the Millennium. Let's take a quick review of the events that immediately proceed the Millennium as this will provide why it was necessary to release Satan.
First the events of Rev. 19, when Christ returns with all the saints and angels to destroy the anti-christ and false prophet. Then in Rev. 20, Satan is locked in the bottomless pit. Why? This is to keep Satan from tempting the remaining people living on the earth.
The Bible teaches that 2/3's of all Jews living during the 7-year tribulation will die, with the final 1/3 entering the Millennium. You can find the details in Zechariah 12 -14. The entire 1/3 will be true believers. Israel becomes the light to the world as God designated her to be and Christ as the Son of David, is anointed King to sit on the throne of David forever ruling from the New Jerusalem. This promise is found in 2 Sam.
There will also be gentiles (non-Jews) that survive the 7-year tribulation however there will be a mix of true believers and unbelievers. Matthew 25 explains what happens to these people and the nations.
Let's deal with the people first. Only the true believers will be allowed to enter the Millennium. The unbelievers are all put to death and sent to Hades, the prison for the unrighteous where there is "torment in these flames". They remain there until after the Millennium to face final judgment at the Great White Throne. This is Rev. 20.
Now for the nations which are called sheep and goats. Those that opposed Israel will not enter the Kingdom of Israel's Messiah and those that protected Israel and the 144,000 witnesses will be welcomed into the Kingdom along with several designated past kingdoms and people that are not in existence today, like Assyria. You can find that in Ezekiel, the 144k in Revelation, and the nation judgment in Matthew 25.
Now that we have the proper setting, let's answer the question directly. Each of the ages are actually for the revelation of the attributes of God, the unveiling of God's reconciliation plan, and complete annihilation of sin - meaning that it will never again be possible for any of God's creation to sin. This is what the Bible deems the consummation of all things. The marriage of the Holy God to His now holy creation. Why is it holy? Because it remains in the state in which the Most High God created it.
Each of these ages require true testing. The test of the Millennium is to show creation that you can put a sinner, the unbeliever, in the best environment and they will still hate and rebel against God. During the Millennium, Christ will rule with perfect righteousness, justice, and holiness, yet the babies born to true believers will be birth with their old sin nature. Although Christ will rule with a rod of iron, meaning that sin will receive swift, just punishment, even death. You can find this written in Isaiah, Ezekiel, and Jeremiah. The world will be converted into the garden of Eden and there will be no want for anyone. The world and its government will be perfect as the government will be upon Christ's shoulders as stated by Isaiah.
Yet, lurking beneath the scene, in the hearts of those who reject Christ as Savior will be this deep seated hatred of this "tyrant" who demands faithfulness, holiness, and worship. Some people will come to believe in Christ and they will camp around Jerusalem (Rev. 20) never wanting to leave their Lord, Savior, and King. However the majority, approximately 95% secretly, so they think hate Christ, nevertheless because the "obey" though unwillingly, they live for the entire 1,000 years.
You may ask, in a perfect world? Yes, my friend! That's the point. The sinner hates God and everything about Him! This happens even with the devil and all demons locked away for the entire duration. This is how evil men are without the Devil's assistance. Fallen man does not need outside temptation or influence to be completely wicked. It's his nature.
When the Devil and demons are released after the 1,000 years is concluded, he convinces all the unbelievers that they can over through God and kick Jesus off the throne. But they miscalculate not understanding that Jesus is the Creator and He instantly calls down fire from heaven that devours them all. Rev. 20
Jesus destroys the heavens and the earth then create new heavens and a new earth wherein dwells only righteousness forever. Yes, there will be natural people living in the new heavens and earth but that's another topic.
Hopes that help.