Why not just use Cloudflare Access for this? It’s the same thing for even less work (and it’s free for personal use).
As far as I can tell, Cloudflare Access doesn't allow you to run arbitrary code in an environment that isn't exposed to the user, which is kind of the whole purpose of this setup. The sole purpose of the OAuth part of this operation is so that the user doesn't have to type in their email. Session persistence/selective access isn't relevant here, and that appears to be the only thing the Cloudflare Access really offers.