HTML TADS was first introduced in TADS 2, and is a way of authoring TADS games with a basic form of HTML. Note that HTML TADS interpreters do not have to use an actual web browser to play them; as far as I know none of them actually do. HTML TADS games can generally also be played in non-HTML text mode interpreters, but with limited formatting of course. This includes the Glk port of TADS found in Gargoyle, Parchment, and Lectrote.
WebUI was the first way of getting TADS games online, but it required games to be compiled specially for it, and it needed a dedicated server to run the games. You could still set up a server, but it would be a lot of work, and I don’t think anyone in the community has the personal expertise. And now that Parchment can play TADS games there’s little need. Consider WebUI dead.
My long term goal is to add HTML TADS support to the Glk port. It should be possible, but it will take a lot to get there, and there are other things in the priority queue.