I think on AndroidTV, TvSettings is used and that is why the bluetooth device works better.
Tablet Android firmware might not have the TvSettings app and the user might be using the green normal Settings app and it might have a bug with certain bluetooth devices, not sure.
Can perhaps check if tablet firmware has TvSettings and if not add it so user can test it.(Might need to remove the normal Settings app since it might cause problems)
I added a menu to TvSettings to open normal Settings app also on AndroidTV firmware and changed the priority of normal Settings app to lower values so TvSettings are used by default in Androidmanifest.xml file.
For AndroidTV - App problem
Choose the top Gear icon to open TvSettings
Go to Apps
See all apps
Click on your installed app
Scroll down to the last Setting - UI Mode
Change the UI Mode to Normal, Desk, Car, Television, Appliance, Watch or Vr-headset.
The default value is Television except for some apps that are already in a whitelist like Amazon Prime Video, Google Movies(both of which are Normal and not Television)
Try to clear cache of your app, grant it all permissions and then change the UI Mode to Normal or Appliance and test again.
This will make the app use tablet UI and not AndroidTV(Television) UI interface and might fix the problem.
If this still doesn’t work then the app might check permissions in /system/etc that is only available in tablet firmware and which is different in AndroidTV.
A logcat will show which permissions your app needs.
Also upload a link to the app if you can, perhaps we can test it to get it to work.
Are you using this app and the latest version?