On both mobile and desktop Safari, tapping/clicking does nothing to speed up a combat turn. I thought it simply might not be implemented, but I saw other people reference doing it, and it does speed things up properly on the initial “getting attacked” screen before the combat starts.
I have animations off, but having them on did not fix the problem (the problem is why I turned them off—they made combat even slower since they couldn’t be skipped). This is causing combat to be very slow and frustrating because everything spends a few seconds slowly popping up text and pausing before the continue button appears. I love adventuring (it’s a big part of what got me into the game), but the sluggish default pace of combat is driving me slightly up a wall.