There's no good way around that unfortunately. The proxy could build in an OAuth client for the major providers, but it's unlikely that this would be trusted by default without significant effort being put into review processes.
As the readme explains, there's nothing to stop you using the existing OAuth client details from another source (such as the many already trusted open source email clients that exist).
Yes. I'd argue the problem is not on the project's side, it's on the Google side (they have ridiculously high requirements for registering OAuth clients for IMAP/SMTP use, especially for a small open-source project).
The provider might notice that their key is being used in an unauthorized way and terminate your account, prosecute you for computer fraud and abuse, etc.
I think this is the only assured way to interop, as I expect Google may try to kill other competing apps (specially in mobile) that does not capture user data or generate data points for its ads.
I wonder if any intentional limitation here should not trigger some of the EU Digital Services Act provisions for interoperability ... in this list [1] I see Google Play, Maps, and Shopping but not GMail!
As the readme explains, there's nothing to stop you using the existing OAuth client details from another source (such as the many already trusted open source email clients that exist).