Is it possible to somehow get 2FA for my e-mail accounts even if they're hosted on custom / private domains? (e.g firstname.lastname@example.org and not gmail)
I think, you expect to enable 2FA on your web server not in web site. It is possible on Apache server, when you use ssh.
I think below link will be helpfull for you.
If you are running the server, then yes eg: https://www.wikidsystems.com/support/how-to/how-to-configure-webmail-for-wikid-strong-authentication/. If not, then no.