Controlling the address is key to switching services and not being shut off for ToS violations.
I wrote about it more here https://meagher.co/own-your-email/
I am trying to move away from gsuite. The thing with forwarding from there is that it goes through spam there first, meaning you really have to check it (my accountant screwed up their spf records recently, leading to a lot of confusion). Using the account directly sucks, you have constant switching and gsuite accounts can't do things like family sharing.
Forwarding services, even implementing srs still can't rewrite dkim, so you get weird reply to addresses than again often trigger things ending up in spam.
I think the best solution while keeping everything together in the Google ecosystem (drive, docs, calendar, etc.) is probably an external provider you do pop from to your standard Google account, then offlineimap style backup Gmail somewhere else. Then you still have arbitrary delays in fetching!
Basically, everything is terrible.
If you're on paid G Suite, you can tweak the Default routing setting [1] in Google Admin to forward all emails to a different domain.
I believe this bypasses Gmail's spam filter (Google might reject some mail during SMTP — I've never had a problem with mail delivery to Google though, unlike to Hotmail).