Important: I didn’t create this project, I just think it works pretty well for my usecase
I do know that Betterbird, a fork of Thunderbird, has a systray icon for Linux, but I don’t require the few power user features that Betterbird adds, and the developer is pretty hostile towards Thunderbird (despite their project being a very close fork of it).
On the Arch Wiki, systray-x was mentioned as an option, and it works really well! (Birdtray is another one mentioned by the Arch Wiki, but it hasn’t been updated for 3 years, so I went with systray-x.) It’s pretty customisable as well, it’s very easy to change the icon as well as the behaviour for startup, minimising, and closing the window. It has also been packaged in the official Arch repos, which is always nice (the repos are usually more reliable + often faster than the AUR), as well as for other distro families too. It looks like there are separate versions for KDE (what I’m using) and GNOME, which is neat!
It is a little janky though. For instance, if you select startup in tray, it opens the full window before minimising to the tray. It still works quite well for me though!
edit: Forgot to mention one thing, you need to force Wayland for Thunderbird for systray-x to work on Wayland desktops!
You can mininize them in their own workspace ( or keep them open in their own workspace) and you will get notifications for them still.
That may be a good option. It’s a minor pain, but mostly just because the email notification has been down there for like ~20 years so it would be nice for it to still be there, but it’s definitely not a show stopper.