Chargeable Appletv remote

The latest Siri Remote uses USB C (while the older used lightning), so you would need that cable and ideally a power adapter to plug into the wall. It then takes about 3 hours to fully charge.

I upgraded my unit in November, out of the box the remote came with a fair amount of charge and still lasted around 3.5 months before I needed to plug it in. I had a spare cable and power adapter, just plugged it in and it charged fine.

Charge the Siri Remote - Apple Support (CA)

If your Apple TV 4K was the previous model (from 2021) or the original (2017) then that did in fact come with the 2nd Gen or 1st Gen Siri Remote (with lightning). However, if you purchased any replacement remote after Nov 2022 then it would likely have been the current 3rd gen remote (with USB C).

I have had both, only the cable used to charge will be different but the procedure will be the same (both are outlined in the article linked above).

You can try the repair, also try different cable and power adapter. If plugging into port on computer it will also likely take longer.