That's what made me extract myself from Gmail. I created my new email address and forwarded my Gmail account to it, and then for every email coming to the Gmail address I updated the sender with my new address. It took me about six months before all my important mail was using my new address, but it actually wasn't that hard and I feel hugely less vulnerable to Google's whims.
Edit: At the same time I also started using a proper password manager, making me again much less vulnerable to losing an email account because I no longer rely on resetting passwords to get into my multifarious online accounts.
This does not solve the fact that your email archive is in gmail though.
The program to do this is called offlineimap.
I have my bank statements in an email account by a provider that is unlikely to ban people for questionable and unrelated offenses.
(You can totally get banned from Google's entire platform if you do something wrong on the Play store after e.g. being pressured to do so by your employer.)
Most of my private email communication (which has dwindled to a tiny number of messages per month) is on GMail.
I've also got a couple other addresses in addition to that. I also have email addresses on my own domain, but I don't know if I'm going to keep that domain forever, as it costs a lot of money.
Devil's advocate: that possibility strengthens your position when your employer tries to pressure you to do something neither you nor Google find acceptable.