As someone that works in AV for exactly your type of scenario… you unfortunately won’t find anything that supports >1080p60 for under $500. That type of video bandwidth is at a premium for switching on KVMs, matrixes, eg. Good USB 3 support is unfortunately expensive, too.

Expect lots of noticeable lag, too. Switches aren’t engineered for gaming yet.

I’ve used SMS Backup & Restore for several years to do exactly what you describe.

Everything backs up to a local folder on my phone and I sync to my home server. The app can sync backups to a cloud storage, but it isn’t required.

Would this be able to process an already downloaded library of channels?