I think whether you have gridlocked pawns in the center or an open game, the center plays a vital role. centralization of your pieces is pretty important in the endgame. all your pieces radiate from the center and exert most power there in most cases. IMO, the center is always important, however how you treat the center changes as you reach endgame.
At what stage of the game when you stop thinking about center control?

Do you consider central control in the mid and end game or is it only important in the beginning?

Do you consider central control in the mid and end game or is it only important in the beginning?
Central control is always relevant. Centralized pieces are active pieces.

Whether or not you need to be controlling the center is another one of those "it depends" questions. It's usually a good idea, but sometimes it doesn't matter, and other squares are more important. For example, if your opponent is trying to promote a pawn, the key squares to control are the ones in front of the pawn.
Do you consider central control in the mid and end game or is it only important in the beginning?