I don't know about Mutt, but I've had no problems handling multiple accounts with mu4e on Emacs. `emacs`/`emacsclient` can be forced to use the terminal by using the `-nw` option.
isync/`mbsync` can also work with multiple accounts. Although, this program just sync's an IMAP account with a local Maildir that clients like mu4e can use for reading mail offline. It's an MRA[1] rather than a whole MUA.
There are many other terminal email clients you can also try.
> Email servers are starting to use more complete auth mechanisms that don't work well with mutt.
Google can support standard auth by activating 2FA, then making an app password. You can do this here:
https://myaccount.google.com/security
Google specifically needs "more complete auth mechanisms" because its regular password gives access to much more than an email account, since Google accounts are a huge platform. What other servers are moving away from standard auth mechanisms?