Instead of editing a package-owned file in /usr, you can instead copy it to ~/.local/share/accounts/providers/google.provider, and edit the ClientId/ClientSecret there. It will override the one from /usr. This should work on immutable distros. It also won’t break next time the package in question is updated and overwrites things in /usr.
You can also create your own ClientId/ClientSecret, instead of hijacking the Gnome one. Unfortunately it’s a bit involved, but the Rclone developers have a step-by-step guide.
Unfortunately, it looks like discussion here is spread across Discuss, Invent and Bugs. I suspect Bugs is the right place for this to go, as oswald_c suggested.