How to convert positions like this.

for this game specifically, checking the engine, Mr. fish suggests, rather than 22.Rae1, I should give up my pawn advantage ( which was defending my passed pawn?? ) for no apparent reason? with a +2.5 eval?? it just feels like I would unnecessarily weaken my passed pawn.
practically speaking, how exactly am I supposed to press my opponents in such positions? and what could I have done better in this game?

#1
"win further material" * 1 pawn is enough to win, you do not need to win further material

"simplify into a winning endgame" * That is to strive for. You did well up to move 29.

"overextending" * 29 e6+ is overextending, just 29 a3 to protect pawn b4

"letting my opponent capture all my pawns" * That is bad. E.g. 30 a3 protects pawn b4.

"rather than 22.Rae1" * 22 Rae1 was fine: you hold your winning advantage. 22 d6 or 22 Nh4 are good alternatives.

The line preferred by Stockfish after 22. d6 appears to be based on the strength of the d pawn. Once it occupies d7, on the verge of promotion, Black is tied down to defence.

White's progress after that is gradual so it doesn't initially look threatening to us mere mortals but there comes a time when further weaknesses are created and more Black pawns drop off.

What strikes me is that you were dropping pawns all over the place looking for a tactical knockout.
So for this sort of position, slow down, protect your pawns, improve placement of pieces, and only then use central pawns (&extra pawn) to slowly restrict opponent.
In time your position will then control more of the board and get easier to play and opponents fewer squares and harder to defend. Then something tactical will turn up.
Just my ideas, Bill

I'm actually an expert at converting winning positions. Converting them to a loss, that is.

I would like to say, that even though engine does not call gf3 a mistake, I feel like it reduces your winning chances because you won't be able to take advantage of his comparatively weaker king. Even after Queen exchange, you are supposed to improve the position of your king, while saving all the pawns. Then slowly squeeze out a win.

Practically, if you see the last few moments of the game, he is playing with an extra piece which is the king. In endgame, an active king is just as valuable as a knight or a bishop, if not more.