I am asking if there is a specific rule in chess regarding stalemate after pawn promotion, other than "the opponent cannot make a move".
No, there are no special rules for stalemate after promotion, nor are there special rules for draws after promotion. The only reason promotion affects whether the game is a draw or not is that it changes the pieces on the board.
Article 5, "The completion of the game" in the FIDE Laws of Chess defines how the game is won and drawn. Stalemate is not the only way the game can end in a draw. This is what it says about drawing the game:
5.2.1 The game is drawn when the player to move has no legal move and his king is not in check. The game is said to end in ‘stalemate’. This immediately ends the game, provided that the move producing the stalemate position was in accordance with Article 3 and Articles 4.2 – 4.7.
5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.
5.2.3 The game is drawn upon agreement between the two players during the game , provided both players have made at least one move. This immediately ends the game.
In the position you give there is no way for either side to checkmate the opponent. Therefore the position is a "dead position" and the game immediately ends in a draw.
Better would have been to promote to a rook. Then the king would still have had a move, Kg7, but checkmate with K+R v K is possible so you could still have won if you knew how to checkmate with king and rook versus king.