In answer to your question:
Is Paul suggesting that Adam did not directly bring death on all men
but instead each person dies only when they sin by interacting with
You are on the right track, partially.
Adam’s sin did indeed bring death but it was the beginning step. When Adam sinned man left living under God’s grace and protection and chose to live his way via the knowledge of good and evil. Since that knowledge of good and evil was then manifested within each man’s own heart and mind, everyone did what was right in his own mind. That is why before the flood man’s behavior was nothing but evil continually.
After the flood, God then issued a single standard of righteousness (the Commandments and the Law of Moses) so man could understand God’s standard for perfect behavior. So the OT covenant of the Law became the initial way you sought God’s righteousness in order to obtain a relationship with Him. However, we understand that God did not intend for man to live by the law since He states in 2 Corinthians chapter 3 that the OT covenant of the law was designed by God to fade away just like the glory on the face of Moses.
2 Corinthians 3 (KJV)
6 Who also hath made us able ministers of the new testament; not of
the letter, but of the spirit: for the letter killeth, but the spirit
giveth life. 7 But if the ministration of death, written and engraven
in stones, was glorious, so that the children of Israel could not
stedfastly behold the face of Moses for the glory of his countenance;
which glory was to be done away: 8 How shall not the ministration of
the spirit be rather glorious? 9 For if the ministration of
condemnation be glory, much more doth the ministration of
righteousness exceed in glory. 10 For even that which was made
glorious had no glory in this respect, by reason of the glory that
excelleth. 11 For if that which is done away was glorious, much more
that which remaineth is glorious. 12 Seeing then that we have such
hope, we use great plainness of speech: 13 And not as Moses, which put
a veil over his face, that the children of Israel could not stedfastly
look to the end of that which is abolished: 14 But their minds were
blinded: for until this day remaineth the same vail untaken away in
the reading of the old testament; which vail is done away in Christ.
Hence Adam’s sin, opened the way for the OT Covenant of the Law which was only temporary, only to be eliminated and replaced by the sacrifice or Christ and the NT Covenant of Grace.
Paul, in your referenced passage, is speaking of attempting to live under the law and attempting to seek salvation by keeping the law. If you seek to attain righteousness through your works and deeds, then you are destined for destruction for no one can keep the law.
He states in verse 8 that apart from the law sin lies dead. That means if the law is not applied to your life, then there can be no sin. That’s why he says in verse 7 that if it had not been for the law, we would not know what sin was. The law highlights sin; it provided a standard in which to judge someone’s behavior. Sin is a transgression of the law.
1 John 3:4 (KJV)
Whosoever committeth sin transgresseth also the law: for sin is the
transgression of the law.
So, in verse 9 he says that when the law (commandment) came and was applied to his life, sin was then activated (since there was now a standard in which to judge his behavior) and then he died, since no one can live through keeping the law. In verse 10, he says that the commandment deceived him. This means that attempting to live by the law seems to be the right thing to do, it seems like a good way to approach God. However, it deceives you because if you offend in only one point you are guilty of all.
James 2:10 (KJV)
10 For whosoever shall keep the whole law, and yet offend in one
point, he is guilty of all.
No one can live by the law since you must be 100% perfect all the time and not sin even once; an impossible condition. So, again, if you attempt to seek salvation on your own without the grace of God and the sacrifice of Christ to “cover” your sin, then you are destined for failure and you are destined for spiritual death; for all of our righteousness is nothing but filthy rags before God.
Isaiah 64:6 (KJV)
But we are all as an unclean thing, and all our righteousness are as
filthy rags; and we all do fade as a leaf; and our iniquities, like
the wind, have taken us away.