It probably wouldn’t ever happen in a real game, but I think it’s possible to be in a situation where you’re still losing after promoting to a queen, but underpromoting to a bishop forces a stalemate by leaving you with no legal moves no matter what your opponent plays in response.
Indeed it wouldn't happen in a game but ... I easily created a position where promotion to a bishop is stalemate after any black move (confirmed by Stockfish):
White pawns on a7 and b7, king on h8. Black king on f2, bishop on g3, rook on h3, knights on a6 and b8, pawns on c6, d7, f3, and h2.
This position is a draw after a8=Q or axb8=Q but that is easily remedied by adding black pieces, e.g., a queen on h4.