Then stop entering your old email address anywhere. If you notice yourself typing your old address, migrate the account to the new one. Eventually all the accounts that you care about will be moved over.

I did roughly the same years ago and it’s not difficult. Every once in a while I get a email forwarded from my old gmail but it’s effectively a complete migration.

Thunderbird with filters does a pretty good job with keeping my inbox clean, although I'm aiming for much less mails anyway.

Emails are like postcards, easily read by anyone who handles them. Just because your mailbox provider isn't google, doesn't mean it doesn't come in contact with google somewhere else.

If you really don't want them to be able to collect the content of your mails then you and all who write to you have to encrypt them. And then you would still have the problem of the metadata to be accessible.