Yes it does!

Not once have I mentioned my equipment, and I know what I have which is a 3rd gen with the latest software. The issue is with Apple’s conflicting documentation on this feature. In the link it specifies this feature working with gen 3, yet there is other documentation which states that if you have a 3rd gen you need to use the remote app. So which is it and why is there a conflict in information?

Ah, I didn't notice the date. They should still update their other material though.

So now that I know that is the most recent instruction from Apple, I would like to use the control center remote with my Apple TV, however every time I try to pair it, my phone shows the 4 digit code only briefly, maybe a second if I am lucky, often less, and even if I remember what code was displayed, and enter it onto my Apple TV using the remote it came with, it says it is incorrect. What now? I have restarted both my phone and the Apple TV, they are both updated, they are both on the same network.

I thought my OP was the updated article, it wasn’t my intention to post the same link twice, but that is the material I’ve been referring to. I don’t know why you are arguing with me about this appearing in a Google search, you don’t know the exact terminology I used in my Google search which very LIKELY explains why you didn’t find it. I’m baffled that you would come out with such a bold claim that it doesn’t appear in a Google search. How many results did you even look through? I found it didn’t I? If I didn’t find it in a Google search then I welcome your alternate hypothesis of how I came across it.

https://support.apple.com/en-gb/HT201664

Your questions are not relevant to the OP.