End game question

en.lichess.org/dvLkXMw9/black#0

In this game, at move 42, Stockfish is calling my Ke5 a blunder and is recommending c4 instead. The way I see it, if I had done c4, it would have simply been a race to promote, with both of us getting a queen but my opponent having both the first move after promotion and an extra pawn. Ke5 gave me the chance of slowing down or preventing his/her promotion chances, which allowed me to promote. What am I missing?

Ke5 might be plain lost whereas Q+P vs. Q gives some drawing chances. You will never be able to do something against the connected pawns so Ke5 is pretty useless.

42...Ke5? loses. The only way to draw was 42...c4!. Yes, both sides queen and yes he moves first after promotion and yes he has an extra pawn, but no that is not enough to win.

In other words: wasting an important tempo with Ke5 and allowing the white king to enter the "square" of the c-pawn was not the best idea.

His 43 h4? was a blunder. He should have moved his king into the square to stop your pawn. His two pawns protect each other.

I guess I got lucky he or she made their own blunder after my Ke5 blunder, then. I suppose that's one of the upsides of being as bad as I am. You play a lot of other people equally likely to make equally egregious mistakes. :)

you just lost a tempo ...