How to be more aware of smothered mate opportunities? I've been playing ChessAcademy's android app for a while when I'm bored: thought it could improve my chess to be solving their tactic challenges (not sure if it's working though..).

One pattern I often fail to notice is the smothered mate. Today, I failed again to notice it while focusing on capturing pieces instead and leveling the score.

The challenge (and solution) is that one:

[FEN "3r3k/6pp/p3Qn2/P3N3/4q3/2P4P/5PP1/6K1 w - - 0 1"]

1. Nf7+ Kg8
2. Nh6+ Kh8
3. Qg8+ Rxg8
4. Nf7#


I failed by thinking of a move that would only turn the piece advantage to my side:

[FEN "3r3k/6pp/p3Qn2/P3N3/4q3/2P4P/5PP1/6K1 w - - 0 1"]

1. Nf7+ Kg8
2. Nxd8 Qxe6
3. Nxe6


Obviously the solution strategy is better, but I failed to see it (as I had in other challenges that included a smothered mate). So I was wondering what "signs" could I be looking for that a smothered mate is possible? I know it might sound a little obvious, but maybe if I start by just trying to notice some small patterns I'll fail less on those tactics and later be able to find more complex moves that set up a smothered mate.
There's a variety of mates that could be called smothered mate, but for what I'd call the "standard" one (sometimes called Philidor's Legacy), like the one in your example, notable signs are (with white mating black as an example):


The black king is in the h8 corner (maybe it just moved there after being checked by the white queen).
The white queen and knight control f7.
The f7 pawn is typically absent but g7 and h7 are still there (g7 and h7 could also be pieces, as long as they don't cover f7 or g8).
The white queen is on the a2-g8 diagonal.
There's a black rook on the 8th rank to do the smothering. (It wouldn't work with the black queen!)


This can be generalized to long castling, but it is less frequent.

Some tactical trainers (or books!) let you practice tactics by theme. I don't know anything about Chessacademy, but one example I know is the tactics in chess.com which has this feature and has a "smothered mate" category (but they use the term loosely!). Maybe after seeing many smothered mates in a row your recognition of them will become more automatic.