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?
To make it seamless so you can still Thunderbird, someone made a Docker image of it here: https://hub.docker.com/r/kebles/wanderbird But, you can probably find a newer release somewhere newer than 4 yrs old like this one. :) The point is, if you are wanting to keep it in the Thunderbird umbrella, then it’s most likely been Dockerized.
I’ve Tried Cypht recently, but if you are using Gmail, it has a conflict there so it won’t work out of the box without some extra work I think.