You are not alone.
I have this problem too. As of March 18th my two brand new AppleTV 4th Gens are getting the same ‘something went wrong’ message. One is a 4K the other is regular hd.
I have 4 Apple TV’s in total. The new one at my office (completely separate location) has the same problem as the new one at my home. I have completely ruled out internet issues, I also have 1000mb internet speed at both my hone and office, and have signed in and out of the app, force-closed and restarted the app, deleted and reinstalled the app, restarted the Apple TV’s. Nothing works.
Oddly my 2 year old 4K 4th gen Apple TV in my bedroom works for the moment, maybe it didn’t download a broken update yet?
Glad to finally know I am not the only one with this issue.