Hey there @Sayuk_Codes!
Public apps are actually meant to be a feature of the Business plan. It looks like you might have actually stumbled across a bug where the feature isn't gated properly so it's possible to access them on all plans 
In general, though, Public Apps don't support any resources that have user-based authentication. If you share authentication between users, either via OAuth2 or a service account, you should be able to use Google Sheets in a Public App:
