How dumb is Carmela Soprano?

Or Richie Aprille went into the witness protection program.

Yeah, and Carmela was probably more clued in than the average mafia wife.

Those guys all lived dual lives with legitimate front businesses (Big Pussy really ran a muffler shop, Tony really ran a waste management business). The wives know their husbands have a lot of "friends" and relatives, and who wants to believe that your lifelong friend or cousin or uncle killed your husband?

She's in denial because of her cushy lifestyle. She also knows Tony is cheating but doesn't care as long as it's not right in her face.

Two words: plausible deniability.

She absolutely knew but didn’t care as long as her lifestyle wasn’t threatened.

didnt she straight up throw away a letter or request for a private eye to look into adrianas death, like right after tony bought her a spec house?

Yup. Like the Jewish doc told her, she sold out

Tony and Carmela go to Dr. Melfi together and then gets referred by Melfi to another psychiatrist. He puts her in her place:

Carmela: His crimes … they are … organized crime.
Dr. Krakower: The mafia.
Carmela: (Gasps) Oh Jesus. Oh, so what. So what. He betrays me, every week with these whores.
Dr. Krakower: Probably the least of his misdeeds.
(Carmela gets up to leave.)
Dr. Krakower: You can leave now or you can hear what I have to say.
Carmela: Well. you’re going to charge the same anyway.
Dr. Krakower: I won’t take your money.
Carmela: That’s a new one.
Dr. Krakower: You must trust your initial impulse and consider leaving him. You’ll never be able to feel good about yourself. Never be able to quell the feelings of guilt and shame that you talked about. As long as you’re his accomplice.
Carmela: You’re wrong about the accomplice part though.
Dr. Krakower: Are you sure?
Carmela: All I do is make sure he’s got clean clothes in his closet and dinner on his table.
Dr. Krakower: So enabler would be a more accurate job description than an accomplice. My apologies.
Carmela: So. You think I need to, ah, define my boundaries more clearly and keep a certain distance. Not internalize my …
Dr. Krakower: What did I just say?
Carmela: Leave him.
Dr. Krakower: Take only the children—what’s left of them—and go.
Carmela: My priest said I should try and work with him. Help him to be a better man.
Dr. Krakower: How’s that going?
Carmela: I …
Dr. Krakower: Have you ever read “Crime and Punishment”? Dostoyevski. (Carmela shakes her head “no.”) It’s not an easy read. It’s about guilt and redemption. And I think while your husband to (sic—sorry, not exactly sure of the dialogue here) turn himself in and read this book and reflect on his crimes every day for seven years in his cell—then he might be redeemed.
Carmela: I would have to … get a lawyer, find an apartment. Arrange for child support.
Dr. Krakower: You’re not listening. I’m not charging you because I won’t take blood money. And you can’t either. One thing you can never say. That you haven’t been told.
Carmela: I see. You’re right, I see.

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Carmela might be quite a few things, but dumb is certainly not one.

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When Christopher dies, she snobs that she can't believe she even thought Liz Lecerva's accusation might be true. She has to be in unbelievable denial to not connect some of these dots, so yeah, in this respect she is dumb.