an error message suggesting that the problem might be with our network connection.
internet connection is ‘good’, 16 mbps.
Apple HD streams are usually below 8 Mbps (average), so if the Roku gets all of that 16 Mbps, then it should be enough.
Something may be causing the app to be unable to contact the remote servers. See if this document has clues that apply to your situation: If you can't watch or stream movies and TV shows in the Apple TV app - Apple Support
“There were errors with this connection” or “check your internet connection” may mean no valid reaction from the remote server.
Verify that your router doesn’t block Apple’s servers (or its CDN) through a firewall setting.
Verify that your router doesn’t block ports that Apple services like to use.
Verify that you use a good DNS on your router, like the one from your ISP, which gets updated with all server names that Apple might use.
Verify that your Roku has the correct date and time and timezone, as Apple may be more strict about that (TLS) than other content providers.
Verify that other users on your home network aren't using the available bandwidth simultaneously.