You don't want to use the groups system. It was once fine, allowing several large and active groups to form, giving them their own subforums essentially to do whatever they want and also moderate themselves. It still had issues (which I'll get to), but it worked.
Later on though, the website UI was redesigned. Everything looked new and fresh (basically, how it looks today still). But some pages were left using the old UI code - the groups system. This caused many issues, because the old UI css doesn't exist ... CSS is the language that controls how exactly webpages look, controlling spacing, borders, whether things should attach to the right or left side, etc. The html was still the old code, but the css and javascript was new. These didn't mix together well, creating a horrible and sometimes unusable UI. Basic functionality like the page2 button on forum posts were broken and glitchy. The textbox to write forum posts didn't support newlines (pressing enter) at all. Many other UI bugs existed too. These were left unfixed for years (and are still unfixed).
Problems with the design of the groups system started showing up. There was no way to search for groups. There were hundreds of groups, with no way to search through them. You couldn't even see if they were active before joining! You had to find out about the groups from elsewhere. Also, there were problems with the groups limit. You could only be in 3 (or 4?) groups at once. Requests to join a group counted towards this limit. There was no way to cancel your request to join a group, you had to wait for the owner to approve it. If the owner was inactive, your request would never go away, and you'd be stuck unable to join new groups.
Groups also became inactive. There were very few active groups, it was mostly just BMN, and a little of TUG at the end.
So the question is, do I fix all these glaring issues? Or shut it down? The decision was easy, shut it down. I don't have the time or interest in maintaining the groups system. I would rather focus on more important things. It was a little sad, I was partially involved in BMN back when that group was active. But BMN has been dead for years.
Right now you can't create groups, but I technically haven't disabled joining groups. But don't even bother, I plan to delete the entire thing at some point. You should instead create a group inside TPT itself, with a save. There has been some success with this before.