Thunderbird will support matrix protocol out-of-the-box in version 102 (due June) and is available in v91 beta now.
I just tried it, you go to preferences, edit config, add a string “chat.prpls.prpl-matrix.disable” and set it to false and matrix becomes an available option in the chats part of your account setup…now to find my old password…
“prpl” (protocol plugin) is the term used in libpurple for a plugin, so it would appear it’s using libpurple as the backend, thus purple-matrix; however, that plugin is deprecated as of a week ago.
edit: I was mistaken, it appears to be using the javascript SDK.
Thanks for the sleuthing.