I have no problems at all with the performance of both my 2022 Apple TV 4K’s, and both remotes work absolutely flawlessly.
As far as the performance of the Apple TV goes, maybe a complete reset would help fix the performance issues you are having?
As far as the issues with the remote goes, get an alcohol wipe and give the remote a good wipe down, especially around the buttons that are sticking. That may help with the issue, if not, the remotes are still under warranty and you could call Apple and much more than likely get a new one sent to you. Pain in the you know what, however, if the remote bothers you that much, go for it.