Google Account IDs differ between OAuth2 and GoogleAppsEngine User API

Question

I have problems replacing an old app because the IDs of Google Accounts differ between the different login options offered by Google.

• Old app: Standard GoogleAppsEngine Java 8 Application using GAE User API
• New app: Nest.js app deployed to CloudRun using Google OAuth2 via passport.js

I verified with many different emails (personal Gmail and GSuite) that both login methods return different Google User IDs - even if the documenation and other resources claim it's unqiue forever and accross login methods.

Obviously I would have expected that the Google Account IDs are independent of the login method.

Is there any way to match or migrate from the old to the new method?