There's no need to search all move sequences, because so many of them end up in the same game state (a game state is a combination of positions and orientations of arrows, with a cut off on positions because far away ones because don't affect whether there's a solution or not).

Of the levels I saw (up to 31), the relevant board area was never more than 20x20 and there were never more than 4 arrows. So the state space had size 16(2020 choose 4) ~= 17 billion. Of course most of those states won't be reachable from the starting state... so the actual number of states you need to explore is probably more like a million or even a thousand.

I think a program could solve all of the game's puzzles in under a second.