Is freemediaheckyeah an IPTV service? Plex or Jellyfin can manage IPTV streams. Plex needs additional software (e.g., xTeVe) to take an m3u playlist and convert it into a tuner.
https://blog.iptvinsider.com/watch-iptv-on-plex/
https://jellyfin.org/docs/general/server/live-tv/setup-guide/
Biblically accurate controller
If there's a sub-$500 tablet that supports Ubuntu and has a kid-friendly case, consider me interested! I'd love to have full control over a video streaming tablet for my kids.
I love the PBS apps too, those will be a permanent install on our kids' devices. I'll check out Epic too.
Like OP, I'll try to avoid the worst of Google Play Store and YouTube Kids for as long as possible. My oldest is still a toddler so we're still in control of what she sees and does. It's inevitable that they'll encounter that stuff at school or other houses, but I hope they'll be disinterested and watching some YouTube slop will only be a curiosity rather than an addiction/coping mechanism.
My wife and I recently rewatched an episode of the original Power Rangers series and my god was that terrible. It was my favorite show when I was 7, but at least it fostered an early love for mecha shows. ;)
My kid got an Android tablet for a 6-hour car ride for vacation. I don't plan to use it unless we're taking a similarly long car ride or hospital stay.
I added a 512GB micro SD card and filled it with downloaded videos from my home server. Most of the time it's in airplane mode.
You could host something like IPTVnator on your Proxmox server: https://github.com/4gray/iptvnator