What does Stockfish do when there's nothing to be done anymore?

I was analyzing this variant of this opening to see what the proper response lines are:

So, at this point, small puzzle, if you want to think about it: Black to move, mate in 4.

Anyways, it continues like this:

At this point there's nothing that white can do to even delay the checkmate. No matter what white does, it will be checkmate in 2. So what does Stockfish suggest in this position for white to move?

a3

Essentially, a move that does nothing, affects nothing, and has no meaning whatsoever. I almost feel like it's Stockifish's way of saying "I resign", because UCI engines do not have an actual way of resigning.

(Of course the reason for that a3 are just technical and serendipitous. But it almost feels like an emergent way for the engine to say "I resign".)