If a pawn is promoted to queen beside the king is the king instantly in check? If a pawn is promoted to queen adjacent to the enemy king, is the king instantly in check?
Per FIDE Chess Laws, rule 3.1, a piece is said to attack an opponent’s piece if the player’s piece can make a capture on that square (and in one more special case not relevant here).  In full:

It is not permitted to move a piece to a square occupied by a piece of the same colour. If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move. A piece is said to attack an opponent’s piece if the piece could make a capture on that square according to Articles 3.2 to 3.8.
A piece is considered to attack a square even if this piece is constrained from moving to that square because it would then leave or place the king of its own colour under attack.

Per rule 3.9, the king is in check when it is attacked by one or more of the opponent’s pieces.
Therefore, as soon as the move is completed, the king is in check.