how do I "stop using apple id" on a specific app
If you are referring to the Sign In With Apple feature this this article has the information about using it.
Sign in with Apple on iPhone - Apple Support
“Change Sign in with Apple settings for an app or website
I hope this helps.
Apps downloaded from the App Store use a sandbox to protect the device from overt interaction by limiting the resources each app request from the device. If the device is logged in with an iCloud account, then the sandbox applicable to your apps are already registered with the iCloud account which was used to download the application form the Apple store. Therefore, there is no way to "omit" your Apple ID from the app since it must have been necessary to download the app in the first place.
If by "stop using Apple ID" you intent to use the device without iCloud, that is possible by singing out of iCloud (your Apple ID) on the settings app but keep in mind the apps already have an associated Apple ID.