That Paul is writing to believers (as he is in all his letters) is not at issue. However, the word 'covenant' (unless I have accidentally missed it), let alone 'new covenant' does not appear in the letter.
Are you suggesting that the exact words have to be there for those believers to be under the new covenant?
The fact that they are chosen in Him through faith establishes a start point of their salvation or do you think people are saved before they actually trust in God?
The words 'long ages ago' is not the best translation. The Greek is pro chronon aionion, 'before times eternal.'
I know that various translators will use different words to express the same concept. But what we do know is that God plan was set before creation.
This is the source of your misunderstanding, I think. Being chosen for salvation is not the same as being saved, just as being chosen for a prize is not the same as receiving the prize.
Christians were chosen for salvation long, long before they were saved through 'sanctification by the Spirit and beief in the truth.' But they were going to be saved, even though they needed to believe. The Holy Spirit set them apart and opened their hearts to believe the good news spoken to them by Paul.
No one was chosen for salvation prior to creation although the plan for how a person could be saved was.
Look at your words " they were going to be saved," was there ever the possibility that they would be lost? Not according to calvinist theory. So when you add "even though they needed to believe." it is meaningless as their faith or lack of would have no impact on their salvation.
The Holy Spirit sets those aside that have trusted in God not so they will trust in God.
No. We see nothing of the kind.
We are told the gospel is the power of God for salvation. So unless the Thessalonians were saved prior to Paul preaching the gospel to them we have to conclude that was what Paul is referring to as "from the beginning".
My apologies for this. I wrote the verse out rather than cutting and pasting it and unfortunately omitted the words in question. I always try to check what I write, but alas, not always accuratly

However, that does not alter the meaning on Eph. 1:4, but rather expands it. We were chosen before the foundation of the world in Christ,
'Whose goings forth are from of old, from the days of eternity' (Micah 5:2, NKJV margin). We were chosen for Christ to redeem, but we were not redeemed until He redeemed us in time.
The whole world was chosen for Christ to redeem, that was why He came so that the world through Him might be saved. Joh 3:17
The plan was set in motion before creation. Christ is the means of salvation. Those that believe will be redeemed. God did not pick out a few select individuals before creation to be saved and the rest condemned as your view requires.
Yep! That's exactly right!

Chosen in etenity, called, saved and sealed by the Spirit in time!
That is just you reading your calvinism into the text again.
You have to ignore way to many verses to hold to your calvinist theory of salvation for a pre selected few.
It is apparent that we see the scriptures differently so we will continue to disagree.
You via your view have God condemning the vast majority of mankind for no other reason than He did not pick them.
I see in scripture that the vast majority of mankind is condemned because they chose to reject the only means of salvation, faith in the God of creation.