Jesus is not only our example how to live in this world, but also the foreshadow of our (the believers) future. Paul summarizes that truth in the eight chapter of the Epistle to the Romans:
For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers.
Just like Jesus is the bright morning star, we shall be too. Just like He is the Son of God, we shall be too (2 Cor 6:18). Just like He sat on His Father's throne, we shall too (Rev 3:21).
To understand 2 Peter 1:19 you can not interpret it independently but must consider the wider context of the whole chapter.
Peter writes to a group of believers, encouraging them to stay on the path of faith and commit to living the same way Jesus did. He reassures them about the reward for their faithfulness.
by which he has granted to us his precious and very great promises, so that through them you may become partakers of the divine nature, having escaped from the corruption that is in the world because of sinful desire.
Peter tells them that Jesus' return is certain, and that he himself foretasted the glory of His coming kingdom on the mount of transfiguration. The trust in Christ's return and our transformation to share His nature should be the leading force in our lives. Until the day of Jesus' return.
The day of dawn when the star is going to arise in our hearts is the same day Paul talks about in 1 Corinthians 15:
It will happen in a moment, in the blink of an eye, when the last trumpet is blown. For when the trumpet sounds, those who have died will be raised to live forever. And we who are living will also be transformed.
The theme of divinization of men is present in both Testaments. As you noticed, the stars in the OT always serve as a picture of the divine being.
In Genesis 15 Abram is told that his descendents will be like stars (quantitatively but also qualitatively). Daniel 12:3 says that after the resurrection, the righteous will shine like stars. Jesus states the same in Matthew 13:43. In the First Letter to the Corinthians, Paul wrote the whole chapter explaining the heavenly bodies we will have after the resurrection. There are obviously some more.
Peter closes his second letter, mentioning the Day of the Lord, on which:
the heavens will be set on fire and dissolved, and the heavenly bodies will melt as they burn.
So one of the reasons for divinization of men is us replacing the rebellious divine beings also known as the stars. God become a man to save us all, but also to make us more like himself.