I used to think that, but I was actually surprised how easy it was to get off GMail. I gave Fastmail my credit card number, clicked a few buttons in their UI to get my mail transferred over, moved my MX records, and I was done. I ended up migrating contacts, too, but that was just a couple more clicks in Fastmail's UI, as they have an OAuth flow that interacts directly with Google's APIs.
I still haven't migrated my calendar, and a few other email-adjacent things, but it's fine; it can all operate this way until I'm ready.
Edit: right after posting, realized you might be using an @gmail.com address, so yeah, migrating off GMail in that case is much harder than if you have a custom domain.
Beyond that, especially given that I assume (hope?) such sites are rare, a simple workaround would be to have a GMail account just for such signups, and set it up to forward to your main mail account hosted elsewhere. I think that's a pretty small price to pay if you really do want to get off GMail.
In my case, I still have my GSuite (or Google Workspaces or whatever they hell they're calling it now) account (really the only difference is now my MX records point somewhere else), so if I did have any sites left where I hadn't switched from Google auth to email/password auth, it would still work.
I only use the products that are very unlikely to go away quickly. Search, Gmail and Android. I'd like to get off Gmail for other reasons, but it's a pain. And I mostly use DuckDuckGo for search these days.