If you selfhost paperless-ngx, there are option to add email accounts and regularly import emails+their attachments like any other document. You can then have it delete imported mail from the mail server, or just move/mark it so you can deal with that manually.

It doesn’t currently support OAuth2 for providers like Microsoft, so you’ve gotta use App Passwords with Gmail for now, but there is a fix in the pipeline to add OAuth2 support soon. (there’s also other methods you can use to get that part working right now)