The point is not to self-host email (not entirely anyway; you’ll always need an SMTP relay with good IP reputation, e.g. mailgun), but you can use a regular web hosting company and buy your own domain there or separately via porkbun etc… Your bank won’t have a clue what email you use, you’re just paying a web hosting co. / domain registrar.
I kinda wish more people would look beyond the big email providers that rely on proprietary apps and tech. Email is a set of open protocols but it was never designed to be secure and never will be. Proton et al can only offer e2ee within its boundary (GPG works just as well if you really need it) - for everything else (most stuff), it’s pretty pointless to try harden that.
For the last 26+ years, I’ve been hosting my email on simple cPanel, with my own domain name, 100% managed by myself. I have a catch-all / wildcard mailbox, get almost no spam (and can blackhole any address that leaks, as they inevitably do), and can access it in my own way (Roundcube, Thunderbird ftw.)
Right now, I use old-fashioned POP3 (so it’s deleted off the server), but could if I wanted, set up a local IMAP server with something like fetchmail and chain it together for more privacy and convenience. (Remember, you’re never gonna approach ee2e levels unless it’s in a proprietary system.) The most important thing; since the hosting company is responsible for email delivery, they use reliable third parties (think mailgun, sendgrid, brevo etc.) as part of the package.
Total control, cheap, and don’t ever have to rely on a big tech company (or a CEO getting political).
Dunno about Posteo or Mailbox but couldn’t really recommend a dedicated email provider as I alluded to earlier - cPanel gives me complete control, although it’s your own responsibility to set up mailboxes and configure it how you like. There’s a way to create a filter to give yourself a catch-all email (use a unique email address when signing up for things), and I turn off SpamAssassin as I prefer 100% deliverability and no false positives. If an email address ‘leaks’, I can simply blackhole it in cPanel.
Used to use Namecheap for domains but now Porkbun (much cheaper). Been using KeePass for a number of years too, but switching over to Bitwarden imminently. :)