New Apple TV Siri Remote not pairing with (last year's) Apple TV 4k

I'm having problems pairing my new Apple TV Siri Remote to my Apple TV 4k (purchased Summer 2020).

Actually, what you are about to read is happening to **both** remotes, since I'm also trying with a second one, also a similar new Apple Siri TV Remote (thought the first one was broken and replaced it).

Followed all the rules and procedures: turned off Apple TV, waited for a few seconds, brought the charged remote close to the TV, made the usual key combos.... etc. etc. etc. as per all the previous Apple TV+remotes that I've owned in the past few years.

Couldn't pair it with my Apple TV.

I just get the annoying top-right notification asking me to bring it closer to the Apple TV, though I've tried every conceivable distance and position, even cleaned the products just to make sure there weren't any dirt covering any sensors and making things worse.

So... couldn't pair two identical new remotes.

I'm guessing this is probably a bug of some kind that will be solved?

Just to be clear: I'm trying to pair the new remote with a previous Apple TV 4k purchased in 2020.

Is anyone experiencing the same symptons?

Thanks!