I think stockfish is recommending you to attack f5 pawn soon with the king by playing Kc4
Stockfish recommends blocking a passed pawn with King instead of advancing it
I agree with post #2. Moving the king towards the e5 square will end all of blacks potential counterplay. The c-pawn is promoting regardless. Preventing black from getting a passed f-pawn will end the game more quickly.
There are no inaccuracies in a pawn endgame. There are only correct moves that keep the assessment of the position as it is (win or draw) and mistakes that cost half a point or more (loss or draw). It doesn't matter how you win as you're supposed to calculate the lines to the end, what matters is that the calculation is correct.

But Stockfish considered c4 to be an inaccuracy and recommended Kc4 instead
That's not true.
Stockfish never uses adjectives like "inaccuracy". You are confusing Stockfih with chess.com's "Game review" (which is utter trash, no one should ever use it).
Stockfish considers c4 the best move, which is forced mate in 14.

Probably because it (Chess.com system, not necessarily Stockfish) wants you to defend the F4 pawn with Kc4, Kd4 and Ke5. Its easier to win this way because you can guarantee that black cannot promote, but it still wins regardless, although you still have to watch out for the king capturing all 3 pawns and potentially promoting.

Probably because it (Chess.com system, not necessarily Stockfish) wants you to defend the F4 pawn with Kc4, Kd4 and Ke5. Its easier to win this way because you can guarantee that black cannot promote, but it still wins regardless, although you still have to watch out for the king capturing all 3 pawns and potentially promoting.
You are overestimating Game review. None of this is even remotely plausible. The glitch is caused by the extreme weakness and shallowness of the engine analysis that Game review is based on.
For reference, here is the game (the position that the OP linked is wrong):
https://www.chess.com/game/daily/763083507
If you just run the pawn, there is exactly zero chance that black can queen.
43. c4 Kxh4 44. c5 Kg3 45. c6 Kxf4 46. c7 Kg3 47. c8=Q
Last move was c4 (from c3). It's clear that I'm going to promote my c pawn to a queen and checkmate my opponent. But Stockfish considered c4 to be an inaccuracy and recommended Kc4 instead. How is blocking my own advancing pawn better than just advancing it? It chided me for c4 as "this loses a pawn", but my opponent is taking the h4 pawn regardless of what I do.