I tried to pair it with the 4k but nothing happened.
The Apple Siri Remote (A1513, A1962, A2540, or A2854) should respond to the pairing attempt with modern Apple TV boxes (A1625 or later), unless the remote is broken or the battery is depleted. There is also a system software version dependency for the A2540 (tvOS 14.5 or later) and A2854 (tvOS 15.4 or later) remotes. Identify your Apple TV remote - Apple Support
using the ir remote does not move to the apps or settings either.
Apple IR remotes do not need pairing with the modern Apple TV boxes (A1625 or later). The old style Apple TV remote (A1156 or A1294) should work automatically, unless it is broken or the battery is depleted. There is also no method to access tvOS Control Center with the old style remote, as it lacks the TV/Home button.
Third party IR remotes have other requirements. Mostly, that needs to be set up, using a secondary functional Siri Remote. Additionally, Apple TV can be learned how to listen to previously unsupported IR remote commands. Use other remotes to control Apple TV 4K - Apple Support