In Rom 3:23 Paul answered the question all including the Gentiles have a sin nature. Having the Law in one's heart didn't equal keeping the entire law.
For whoever keeps the whole law but fails in one point has become guilty of all of it.
(James 2:10, ESV)
Wrong is the absence of right. Evil is the absence of good. While every person probably has some good, they are not perfectly good. Where good is absent is where sin resides. Because no one is perfectly good, all have sinned. What is their conscience accusing them of if they aren't sinning?
while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them
(in Romans 2:15, ESV)
Paul's point was even the Gentiles did not live up to what they knew was right.
For there is no distinction: 23 for all have sinned and fall short of the glory of God
(Rom. 3:22–23, ESV)
Adam and Eve ate from the tree of the knowledge of both good and evil, not just evil alone. Thus, the sin nature did not exclude knowing what is right. It implies that knowing what is right and not doing it is what is sin.
So whoever knows the right thing to do and fails to do it, for him it is sin.
(James 4:17, ESV)
And the LORD God commanded the man, saying, “You may surely eat of every tree of the garden, but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.”
(Gen. 2:16–17, ESV)
Here Paul answered the question that all people have the sin nature in greater detail.
12 Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned— 13 for sin indeed was in the world before the law was given, but sin is not counted where there is no law. 14 Yet death reigned from Adam to Moses, even over those whose sinning was not like the transgression of Adam, who was a type of the one who was to come.
15 But the free gift is not like the trespass. For if many died through one man’s trespass, much more have the grace of God and the free gift by the grace of that one man Jesus Christ abounded for many. 16 And the free gift is not like the result of that one man’s sin. For the judgment following one trespass brought condemnation, but the free gift following many trespasses brought justification. 17 For if, because of one man’s trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ.
18 Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men. 19 For as by the one man’s disobedience the many were made sinners, so by the one man’s obedience the many will be made righteous. 20 Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, 21 so that, as sin reigned in death, grace also might reign through righteousness leading to eternal life through Jesus Christ our Lord.
(Rom 5:12–21, ESV)