I second Unboxious’ recommendation of Ghost in the Shell. You’ve seen Oshii’s movie, so maybe try 2026 version, it’s pretty different in tone, but Major stil remains badass. Also:

• Assassination Classroom – Koro-sensei is quite a role model
• Classroom of the Elite – it’s very edgy, so given that you disqualified Code Geass and Death Note, this might not be to your taste as the MC is that kind of character, just more autistic. Also I’m not sure if I can call this anime good. Somehow I managed to watch a bunch of seasons, but ended up dropping it during the most recent one.
• Saga of Tanya the Evil – Tanya can hardly be called a role model, and we see her struggling a lot, but I cannot deny her competency in what she does if we look at it through the eyes of people around her

I also wanted to mention Jujutsu Kaisen – Gojo is generally a goober, but he’s a menace when he locks in; Amagi Brilliant Park, because it’s a funny take on competency; Lycoris Recoil, because Chisato is such a pro, but it looks like you already watched those.

Generally, it’s hard to find something good that fits these criteria, so pretty much everything I mentioned is stretching your definition of competency, but that’s best I can think of right now