why is this an inaccuracy?

So today I played a game, and I was wondering why 56... a3 is an inaccuracy. When I pressed "Show Moves" all it showed was 57. Kh7 (I dunno what that does though..) I retried the move and apparently 56. Ke7 is best. Does anybody know why though? Shouldn't a3, pushing the pawn to promotion, be best?

Besides, even if Black were to play Ke7, they still win but it takes a bit longer.

In the race to queen a pawn, Black queens on move 4; however, White queens on move 5 while giving check. Game ends in draw. With Ke7, white is forced into "opposition" on g7 or black gains the f-file denying white ability to queen its pawn. White cannot stop Black from queening. With Kon g7, black will queen giving check

Yeah, I believe the engine is practically wrong here. This is just an example of an engine being too much of a perfectionist. Your gameplay was perfectly fine, easily queening and stopping White's f-pawn later. 

The engine is telling me that 56. ... a3 is best

I looked it up on a tablebase (tablebases go up to 7 total pieces, as far as I know, and this position only has 4).

White's f4 was no worse than any other white move at that point (everything was mate in 21-ply), and your a3 was the best move (Kd7 and Ke7 were second best, each delaying mate by 2 moves).

So, basically, it is just a matter of the computer not seeing through to the end of the line, and evaluating one semi-random position (most of the way down) as slightly better than another semi-random position. Computers "trim" lines they calculate because they don't have the resources to calculate all the way down on every possible move; sometimes they do this to the wrong line, particularly if the "right" line is very similar to another reasonable line.

The engine is not wrong here. The engine gives a3 as the best move, and it is (it's forced mate in 11).

What is wrong here is the chess.com "Game review" script that declares a3 as an "inaccuracy" and talks nonsense. The reason is probably the extremely shallow analysis used by Game review.