My question has been answered by Solocutor and I accepted the answer but I wanted to elaborate...
We tend to think of "sin" (ἁμαρτία) as something you do. "All sinned" etc. and of course that's appropriate. But in this section of Romans Paul "speaks in simple terms because of the frailty of your human nature" and compares sin to an evil alien living in our soft tissue:
Rom 6:19 I am speaking in simple terms because of the frailty of your
human nature. Just as you once offered the parts of your body as
slaves to impurity and to greater and greater disobedience, so now, in
the same way, you must offer the parts of your body as slaves to
righteousness that leads to sanctification.
I find it helpful to call attention to the personification by adding "Mr." to "sin" so I hope you will indulge me:
Rom 7:8 But Mr. Sin seized the opportunity provided by this
commandment and produced in me all kinds of sinful desires, since
apart from the Law, Mr. Sin is dead. Rom 7:9 At one time I was alive
without any connection to the Law. But when the rule was revealed, Mr.
Sin sprang to life, Rom 7:10 and I died. I found that the very rule
that was intended to bring life actually brought death. Rom 7:11 For
Mr. Sin, seizing the opportunity provided by the rule, deceived me and
used it to kill me.
Paul says that Mr. Sin is the reason that God's holy law is ineffective in producing righteousness in an unregenerate Jew. Mr. Sin uses the commands of the law to bring about death.
Mr. Sin is portrayed as a slave owner to the unregenerate Jews who embrace the Torah but are conflicted because of the desires within their bodies. Rather than conform to the law they fall into the sway of their owner, Mr. Sin, and cannot obey the law. Instead the commands of Mr. Sin direct their thinking and behavior.
In this light it is that Paul says essentially:
"Mr. Sin extracts painful labor in his service and the only recompense
he gives for it is death; but God gives his freemen everlasting life
But since the personification of sin is a metaphor, for what is it a metaphor? It is a metaphor for "the mind of the flesh", which is in turn a metaphor for the desires of the body:
Rom 7:25 I thank God through Jesus Christ our Lord. So then with the
mind I myself serve the law of God; but with the flesh the law of [Mr.] sin.
Rom 8:5 For they that are after [are controlled by] the flesh do mind
the things of the flesh; but they that are after the Spirit [breath]
the things of the Spirit [breath]. Rom 8:6 For to be carnally
minded is death; but to be spiritually minded is life and peace.
Rom 8:7 Because the carnal mind is enmity against God: for it is
not subject to the law of God, neither indeed can be. Rom 8:8 So
then they that are in the flesh cannot please God.
Please not that I didn't use any of the translations that speak of "sinful nature" for σάρξ because I consider that a bogus invention to skirt Paul's idea that the body itself is full of sin, rather than the mind. Clearly Paul is echoing Moses' description of man being composed of flesh (from the earth) and breath (from the lungs of YHVH):
Gen 2:7 So the LORD God formed the man from the dust of the ground,
breathed life into his lungs, and the man became a living being.
Gal_5:17 For the flesh lusts against the breath, and the breath
against the flesh: and these are contrary the one to the other: so
that ye cannot do the things that ye would.
Rom 7:23 But I see another law in my members, warring against the law
of my mind, and bringing me into captivity to the law of Mr. Sin which
is in my members. Rom 7:24 O wretched man that I am! who shall
deliver me from the body of this death? Rom 7:25 I thank God through
Jesus Christ our Lord. So then with the mind I myself serve the law of
God; but with the flesh the law of Mr. Sin.
Please don't take me to be saying that this is the experience of the regenerate Paul or the saints. This is Paul's metaphor for the vain struggle of the unregenerate Jew. The way to escape the control of Mr. Sin is by the death of baptism:
Rom 7:1 Don't you realize, brothers—for I am speaking to people who
know the Law—that the Law can press its claims over a person only as
long as he is alive? Rom 7:2 For a married woman is bound by the Law
to her husband while he is living, but if her husband dies, she is
released from the Law concerning her husband. Rom 7:3 So while her
husband is living, she will be called an adulterer if she lives with
another man. But if her husband dies, she is free from this Law, so
that she is not an adulterer if she marries another man. Rom 7:4 In
the same way, my brothers, through the Messiah's body you also died as
far as the Law is concerned, so that you may belong to another person,
the one who was raised from the dead, and may bear fruit for God. Rom
7:5 For while we were living according to our flesh, sinful
passions were at work in our bodies by means of the Law, to bear fruit
resulting in death. Rom 7:6 But now we have been released from the
Law by dying to what enslaved us, so that we may serve in the new life
of the breath, not under the old writings.