Can using a washing machine as a water reservoir damage it?
Just conjecture here, but I think you would be fine for a few days. They needs must design for unusual scenarios, like if you loaded it and then lost power before it could drain.

A top load machine rated for 22 lbs. is a large capacity machine, probably about 4.5 cu. ft. If loaded full of water without clothes (we will run with the presumption that it is designed to handle running with no clothes, because that could easily happen, in theory) 4.5 cu. ft. = like 34 gals. (~270 lbs.)

I will not address the concerns I have with actually drinking water that may have residue of detergent, bleach, and all manner of whatever got washed off of stuff. Better than dying of thirst I guess.