You are on the right track with your thought line in regards to “the personification of sin”. In those verses you quoted (Romans 7:11-14) ‘sin’ is a ‘noun’. That distinction is important!
‘Sin’ [verb] is what you ‘do’ [with your body]. ‘Sin’ [noun] is what you ‘are’ - that is, your ‘sin nature’, what Paul calls the ‘Old Man’, and elsewhere ‘the flesh’.
So here in Romans 7, Paul is talking about the ‘sin nature’ - that is, you - so it is personified. ‘You’ in a believers case is ‘the old/previous/former’ you.
The ministry of the Law actually gave sin (the sin nature, see Romans 5:21) an occasion against people. The corrupt rebellious nature of man will always lust for what it cannot have. Forbid people to do something that they were only mildly interested in before, and they will develop an uncontrollable lust for that very thing.
This is how the Law worked. [the] Sin [nature] was already at work in man, but when the Law came, condemning their actions, sin came alive (Romans 7:9) in comparison to what it was before. The reason God did this was because mankind had been blinded to what sin was and its consequences. Sin had already beaten and enslaved people, but they didn’t realize it. They thought they were good enough, until the Law came. Once they were forbidden to do and think certain ways, sin began to abound (Romans 5:20), and they became aware that they were, by nature, children of the devil (Ephesians 2:3) and needed a savior. That was the purpose and ministry of the Old Testament Law (Romans 3:19).
According to these verses, sin actually revives and gains an occasion against people when the Law is used. The right use of the Law is to give knowledge of sin (Romans 3:20) and convince people that they are doomed without a/the Savior. The Law is powerless to overcome sin. Only the grace of God can cause people to overcome sin (Romans 6:14).