If you have your own mail server and view your mail locally on a client like thunderbird, you can’t really view your mail on any machine in which you don’t want to be installing an email client on or one that isn’t yours. Are there any self-hosted webmail options in which you can log into your email on any machine without using a 3rd party service?
Roundcube and SOGo (which is used by Mailcow, but hass fewer features than Roundcube) are the only somewhat modern looking options. All the other stuff looks like straight out of the 90s/early 2000s. Nextcloud Mail is pretty good as well.
There is a guide in the Mail cow docs on integrating Roundcube, that’s the client I use for my stack.