I want a text only client, running in a terminal. I don't care that I won't be able to see the pictures & animations - in fact that's an advantage.

https://weechat.org/ -- supports matrix (as well as IRC).

Yes this is fair. I'm even using Weechat for IRC & Slack, so I just need to get around to setting it up.

The emacs client is nice, ement.el, is nice. And there's probably a weechat plugin somewhere.

It does look and work very much like a web view. I just tried it.

Uh, how?.. It’s a conversation window with a contact list to the left, with GNOME-standard (libadwaita) look and feel. If you want separate conversation windows (like ICQ or Pidgin), then I understand the desire, but it’s pretty much orthogonal to web-view-ness (also very rare these days regardless of protocol).

Maybe Adwaita looks like that, I don't know. But there is a ton of whitespace, lots of clickable UI elements that look just like regular text, that kind of thing.