You’ll easily find solvent alternatives online, such as THIS.
Ethyl acetate isn’t a bad guy (certainly better than other solvents) but it’s not green chemistry or really that renewable aka bio-based. As an alternative, ethyl lactate comes to mind.
BTW I’m not too familiar with making nail polish but the few things I know (basically THIS)… the solvent part is probably the least concern (????). If you want to replace acetone, methyl acetate might work though it’s not that ‘bio’… if ethyl lactate or propylene carbonate would do the trick, I don’t know (slower evaporation).
Replacing the other ingredients… ugh… maybe not using nail polish or oldschool real shellac?