[SwiftyBug]

I was in the exact situation as you are. I moved my custom domain to iCloud Mail. I'm not sure how complete the custom domain is with iCloud Mail. It basically uses the custom domain email to redirect to your @icloud.com email address. In email clients I have to login as [e-mail] and set my [e-mail] email as an alias. It works perfectly though, I'm very satisfied.

My Google account still exists at [e-mail], I can still OAuth with that account. My Gmail inbox is just not updated anymore since the emails are actually going to Apple's servers. I requested a Google Takeout (basically all the files and emails associated to your account" so if I ever lose access to that account, I don't lose the files.

[stranded22]

I migrated from Outlook’s custom email domain to Apple’s. It took a couple of changes with the DNS records and exporting the emails from Outlook.

In Apple, you can change the login details for your account to your custom domain.

Sounds like a project though - I also have a paid Bitwarden account which I use for my 2FA codes. Works well for me