You dumped out the water ten minutes ago. The pot is cooled off, and empty. It only had whole eggs in it, still in the shells. Now tell me, do you wash that pot? Get out the sponge and the soap and scrub it like usual? Or do you give it a quick rinse and slam it in the drying rack? No judgement here, only curiosity.
I have a dishwand that just stays out all the time, so I’d hit it with that. Almost everything either goes in the dishwasher or gets hit with the dishwand. If I cut up something like apples or cucumber I may just give the knife a rinse before it goes back into the block