Gen 3 Apple TV got put into storage for a bit as I was not using it, got it back out recently.
[Apple TV HD, tvOS 16]
The selected relevant device is not 3rd generation, but 4th generation. Is that the device with the issue, or are there two different models in use?
Remote will not connect.
To connect the legacy remote A1294 with Apple TV (3rd generation) [A1427 or A1469], follow this procedure:
If your Apple TV remote isn’t working - Apple Support - Internet Archive
Do both steps, the unlinking and then the linking.

To connect a Siri Remote with Apple TV (4th generation or later) [A1625 or later], follow this procedure:
Pair a remote with Apple TV - Apple Support
Any of the red indicated remote models will work (with tvOS 15.4 or later). Even the two legacy remotes would work (mostly; some functions will be out of reach due to less buttons), without needing any pairing.

No problem, I’ll use my phone as the remote, except I can’t because the Apple TV isn’t connected to wifi. Okay, I go buy a router satellite so I can have a router right next to the apple tv so I can plug it in via ethernet. Done, now the Apple TV is connected to wifi, I connect my phone to the apple TV and bam, I have to input a passcode into my TV in order to use my phone as the remote, well I can’t do that, the remote won’t connect.
For Apple TV (3rd generation), you’ll have to enter the code on Apple TV, using a physical remote.
For Apple TV (4th generation), you can enter the code on the iPhone, a sure improvement.
Go get a second apple remote from a family member who has the same generation apple TV. Attempt to disconnect and resync their remote. Seems to be working, as the light on the front of the TV is flashing, but nothing is working, still have no control of Apple TV.
The blinking status light only indicates that the remote sends a potentially compatible signal that the Apple TV can pick up. It doesn’t mean that the remote is linked or paired yet. Commands from unlinked or unpaired remotes will be ignored.
Spend hours browsing reddit and Apple forums for a suggestion on a fix to no avail, so now I am here, hoping someone can help me get my Apple TV working before the first F1 Race of the season tomorrow.
The F1 TV app requires Apple TV HD (4th generation or later) with tvOS 16.0 or later.
The 3 practice races and position qualifying race were also televised before the actual race, on Friday and Saturday (Australian time AEDT; UTC+11). 02h45m until the race!
As a last resort, one could connect a computer to a TV using HDMI, then access the streaming service in a browser, and use full screen playback.