Why do people think that clipless isn’t something you can get out of. Modern clipless pedals aren’t Cinelli Death Pedals. I mountain bike in clipless where clipping out has never been a problem even on narrow trails that cut across steep slopes. I can clip out on either side as needed and do it quickly enough that I don’t crash.

In your situation, I would likely have clipped out and put a foot done as well. But I might also have been able to use body English to recover the slip so that I wouldn’t end up with wet feet.

On the other hand, putting out a foot to catch yourself is more likely to just result in your foot slipping on whatever your tire slipped on. And, in all likelihood, your foot and bike are going to slip in different directions. That seldom ends well. I’d rather be wet than be broken.