Correlation of Openings to Checkmates

Do certain openings tend to lead to certain checkmates? I mean if a good player understands their opening, understands their plan and is aiming for checkmate attacks according to that plan. Of course, there's many a slip 'twixt cup and lip. The good player will also have plans B and C where the defence avoids the mates but makes other mistakes or concessions in doing so. I am asking this question because in doing puzzles I noticed, or thought I noticed, certain mates coming up from certain openings. I am not simply referring to opening traps here. I am referring to deeper middle game plans and events.

Or do people make the checkmating plans after certain weakening moves by the opponent? For example, an inappropriate or mishandled fianchetto of the king's bishop? Or a mishandled open Sicilian after black plays d6 and e5? Or during a mishandled defence against a Pillsbury knight? Or after mistakes by the opponent that facilitate the winning of a pawn storm race on opposite wings?

I ask these questions, wondering if in playing certain openings, I should also plan for not only making certain attacks but even heavily practice the specific checkmate types more likely to arise from that opening? I guess the same reasoning applies as would apply if learning an opening that can lead to a successful minority attack. Part of that study should, I guess, include study and practice in actually executing minority attacks.

Probably there's no super-specific correlation, but maybe some general patterns: For example, if h7 is a standard move in your opening, you may have to look out for "greek gift" checkmate patterns in some openings. Or, if white plays the King's gambit, as black you need to be super careful about sacrifices and check mate attacks on f7. This kind of stuff.

The correlation between an opening and checkmate pattern is pretty weak. You will see back rank mates arising, for example, from any opening. There are some exceptions such as Legal's mate with the original version being 1. e4 e5 2. Nf3 d6 3. Bc4 Bg4?! 4. Nc3 g6? 5. Nxe5 Bxd1?? 6. Bxf7+ Ke7 7. Nd5# 1–0. This can arise from open games with White or Black but it's hard to see how you'd reach a similar construction with the Sicilian or the Queen's Gambit.
There is a very strong correlation between attacking schemes and pawn structures, like the Pillsbury knight that you mentioned, occupying an outpost on e5 and supported by pawns on d4 or f4. Or in the Sicilian, there are White piece sacrifices on d5 or e6 and Black exchange sacrifices on c3. It's important to be aware of the typical schemes for the openings you play and there's a nice series of books by Gennady Nesis titled 'Tactics in the ....' with each volume covering a different opening. But attacking schemes rarely end in a forced checkmate unless your opponent is cooperative.

Great question!

I suspect so, yes, but definitely certain openings result in more mating attacks, so as a result it would make sense to study typical mating motifs that arise in that opening.

I am only good in one opening, two at most, and hopeless at the rest, but in those couple of openings I definitely know the typical mating ideas.

Some courses, for example on Chessable, also include typical tactics in that opening. Lichess also has a similar feature, but I think that is a bit too generic.