Not an answer but a follow-up question: is there open firmware for TVs like Openwrt for routers? I have never heard of such a project, but it sounds like it would be useful.
That project has fallen victim to people losing interest. A section for 2011 model year TVs has WIP tags for the last 9 years. This might as well have a perpetual under construction shovelling man GIF.
Software on TV (and worst, set top boxes) is awful is due to the fact that it is an under power CPU and limited memory. The app you saw is either web app in Webkit Embedded or similar embedded, Android app (Android TV) or Roku brightscript app.
Most of these TVs run Linux. This lawsuit by Software Freedom Conservancy is aiming for eventual creation of an OpenWRT-for-TVs project (similar to how an earlier lawsuit created OpenWRT).
TBH though, we don't need another distro specific to certain hardware types, instead we need standard distros like Fedora and Debian to support TV hardware and use-cases.
https://github.com/RootMyTV/RootMyTV.github.io