I have not used this Apple TV in some time so its TVOS version is probably a bit behind
Siri Remote (2nd generation) [Lightning charging port] requires tvOS 14.5 or later.
Siri Remote (3rd generation) [USB-C charging port] requires tvOS 15.4 or later.
Apple TV remotes and their compatibility - Apple Support
Try using the software remote on iPhone or iPad, if you have one of those, to do the needed updates first.
Else try restoring and updating through a USB-connected computer.
If you know someone with a black Siri Remote or old style Apple Remote (aluminum) A1294, then see if you can borrow that for a bit to do these updates.
Else contact Apple about not being able to do the updates. They may refer you to an Apple Store or Apple Authorized Service Provider for further assistance.