That is not going to work. Other remote can be learnt but you would still need the original remote to set that up. Since it’s attempting to mimic the Apple remote there is no guarantee it will even work at all. At any rate, you will need to purchase an official remote from Apple and then I would recommend restoring the unit. Be aware that the 3rd Gen is discontinued, doesn’t have an App Store like the 4th and 4K models and won’t have features associated with the current TVOS platform (Apple Music, iCloud Photo Library, airplay 2 etc)
As you found out, for 3rd generation, you still need a physical remote to navigate the menus to complete the setup of the iOS Remote app. But you should be able to use the physical remote, if you unlink (any setting for previous remote) and link again (new remote):
If your Apple TV remote isn’t working - Apple Support
Unlink and link again, like this:
Apple Remote (aluminum)
- Unlink your Apple Remote to your Apple TV. On your Apple Remote, hold down Menu and Left for six seconds. Then on your Apple TV, look for
above an icon of a remote. - Link your Apple Remote to your Apple TV. On your Apple Remote, hold down Menu and Right for six seconds. Then on your Apple TV, look for
above an icon of a remote.
I’ve tried the method you suggested, first holding “menu” and the left button to unpair the previous remote as well as “menu” and the right button for 6+ seconds each. Did not work. I should have mentioned the remote is not a genuine Apple remote. It’s a generic version that was advertised as being a clone for the original. Instead of aluminum it is made of plastic. Does that make a difference?
I should have mentioned the remote is not a genuine Apple remote.
I have no way of knowing what its limitations are, or if it works at all.
Apple TV Remote App & 3rd Party Remote