Not convenient. My computer is actually a docked Steamdeck I only use occasionally in Desktop mode. I know lots of people will frown at that, but I do 99% of anything I do (aside from gaming), on my phone since a long time ago. For work I have a work laptop and I surely wouldn’t want to store my mails there.
So having Thunderbird on my Steamdeck for browsing old e-mails is just not convenient for me.
My small homeserver is part of a backup strategy, so putting something on it reachable via a webUI of some sort will also ensure all of that is backed up. Since my Steamdeck is mostly games and many saves are stored in the cloud automatically, I don’t back it up as much, not worth the effort.