Is there any use for promoting to a rook or bishop instead of a queen?

Or may be you should learn the elementary checkmate and stalemate positions, there's only 17 in total. You should also be familiarise yourself with the elementary mating methods starting off with of K+Q vs K, K+R vs K (opposition and rectangular methods)

Recommended reading

Basic Chess Endings ( Reuben Fine) and/or Fundamental Chess Endings (Muller & Lamprechet)

You accidently underpromote to a knight on the second puzzle in Puzzle Rush...

Depends on how severe the time pressure is (particularly if there is no delay or increment).  If you immediately see a simple ladder mate with a rook that takes only a handful of moves then for practicality there is no reason to spend precious seconds seeing if there is a more elegant or faster mate with a queen promotion that will not be a stalemate.  When I see a mate in five I don't spend my time trying to see if it can be done in three, but rather spend time simply verifying it really is a mate in five.  I'll take the teasing over missing a faster win if I've already secured a certain win.

Fine's book is still good, particularly if you get the corrections for what were eventually found to be some errors.  The real value isn't necessarily the exact tactics, but rather the ideas behind them.

What I'm saying is that rooks don't take diagonally. In the past, while attempting to checkmate I've stuck a queen on a square not realising their king has no place to move and it pops up stalemate so sometimes I only promote to a rook when I'm clearly winning just to avoid throwing the game away.

Firm but fair and you're absolutely correct. My point is knowing the elementary 9 stalemate and 8 checkmate positions will help you to calculate the end game better, instinctively and most importantly faster.

Yes, Fine's Basic Chess Endings was written in 1941 and pre-dates chess engine verification. I have 1969 and 2003 copies, the 1969 copy contains inaccuracies but I've yet to find any in the 2003 copy although my go to endings book of now is Fundamental Chess Endings.

Mostly it's when queening causes stalemate, other times it's when a Knight would fork their queen/king or cause checkmate. The stalemate can be cause by a tactic also.

You can actually do whatever you want.... just don't stalemate

Such as

Black Ka8, Nb7, Pb7 Rg6

White Pb6, Pd7, Pe7, Pf7, Ph2, Kh1

d8=Q is not a stalemate, but ... Rg1+ forces Kxg1 and a stalemate (if the White pawn was on h4 instead of h2 it is a super-rook situation with the Black rook moving to g1, g2 or g3 to keep checking the White king).

If d8=B is played instead then the e and f pawns can be safely queened.

Yeah sometimes you are in such a position that if you promote to a queen, it becomes a stake mate while other chances are the you can give a check mate by under promotion like promoting to a knight.

Done!

Promoting rook or Knight instead of queen is useful sometimes (stalemate ideas, skewer), but promoting bishop is very rare useful. Best regards