As long as the nail polish is completely dry and there aren’t any other glues or glitters involved etc you’re fine.
Nails are a big hobby of mine. Dry polish is no biggie to go in the tank, as long as it’s not chipping off and getting in the water I guess.
I only do my nails on a day I know I won’t be dipping my hands in the water, to be sure no acetone or any residue of anything gets in the water. That stuff evaporates quickly but stays on your skin for longer than you might think.