Touch pad on remote control for AppleTV 4K getting slower to react
➥ Re-pair the remote with the Apple TV device.
I did this inadvertently. After getting even worse behavior, the remote became unusable, even after restarting the Apple TV. So I purchased another Siri Remote.
I paired the new Siri Remote by simply pressing a button, and holding the remote physically close to the Apple TV device. New remote worked well. So out of curiosity, I re-paired the old remote simply by pushing any button and then holding close to Apple TV. Two things happened:

The old Siri Remote works well again! After being re-paired with the Apple TV device, the old remote works just like new. The pairing process seems to have fixed the problem.
The new remote was no longer paired. Pushing any button starts the pairing process. So you cannot have more than one Siri Remote connected at a time. Bummer.

If anyone else is having this problem with their Siri Remote getting cranky and slow, try re-pairing. I do not know how to un-pair an existing remote unfortunately, except by buying the new remote. Rather than buy, perhaps borrow a friend's Siri Remote to pair and then re-pair the old one.