There are no channel / plugin groups in the side menu

Plex has dropped support for those content plug-ins quite some time ago… this was announced over 2 years ago.

https://www.plex.tv/blog/subtitles-and-sunsets-big-improvements-little-housekeeping/

:skull: Plugins : This was not a decision taken lightly, as they’ve been around for a long time, and we’ve had good times both writing and using them. But bluntly, hardly anyone uses them (less than 2% of users), the ancient protocol they use is a continued pain for clients to support, and if we were to build the feature again, we’d do it very differently in this day and age. For utility-type functionality, we love standalone apps like Tautulli and believe this is a better approach. But don’t panic—while the Plugin Directory will soon be gone, you can still manually install plugins for the foreseeable future.

You might still be able to install them, but they will no longer show in the main menu nor play any content.

What you’re seeing in the 2nd screenshot is a relatively new online media source offered by Plex:
https://support.plex.tv/articles/free-live-tv-streaming-overview/