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.
A quick rinse’ll do’er.
No washing, the boiling water sterilized anything nefarious on the eggs. I don’t wash my cast iron either, just rinse and kill it with fire on the stove.
quick rinse for me
I leave the pot on the counter for five days, forgetting its contents were harmless, and then wash the pot.
Did you wash the poo off the eggs before you started? If so; then, yeah, rinse it out and hang it back up.