Your project has 638 physics constraints, 778 bones, and it clips 13,966 triangles. That is a lot to do in one skeleton, and the clipping is especially performance heavy. You may have trouble putting this in a game if you are exporting data. It's OK if you are exporting images/video.
It is slow because auto key is checking everything to see if anything needs to be keyed, and there is a lot to check. We've improved this to be more efficient in 4.3.13-beta. If you turn off auto key, it is much faster, and then you can key with K for Key Edited, which keys everything that is edited. That's the same thing auto key does, but pressing it once after rotating the bone is faster than doing it many times as you rotate.
Also turning off clipping will improve your FPS. You could consider masking with a large image instead (uncheck Export and Select for that image). If exporting images/video you can specify the crop position and size, so you don't need clipping. If exporting data, at runtime you can mask or allow the parts you don't want shown to be drawn off screen.
