What Linux setup works well for a living room media PC?

Take a look at Bazzite with Plasma Bigscreen. Bigscreen is the part aimed at a TV-friendly interface, so it is closer to the tiled setup you are after than a normal desktop.

Kodi is another frontend worth looking at for the media side. You could use it alongside a browser for anything you prefer to open on the web.

You don't necessarily need a special media distro. Debian with automatic login and Firefox opening full screen can be a pretty simple setup. Save your Plex and YouTube tabs and use an air mouse to get around.

That won't give you the same tile interface, but it keeps the setup fairly straightforward if a browser does everything you need.

For YouTube specifically, check out VacuumTube. It is available on Flathub and is designed for a couch-friendly YouTube experience. You can pair it with whatever distro and Plex setup you like.

Pop!_OS is another option if you would rather have a regular desktop that is easy to use. It is less of a dedicated TV interface, though, so a remote-friendly frontend or an air mouse may make it nicer from the couch.