The Apple TV Remote/Siri Remote wouldn’t show up on your Mac. It doesn’t interact with the Mac, other than taking some energy through its power circuits.
You can monitor the charge on the TV screen connected to the Apple TV box, through Apple TV Settings. Or else go by time:
Assuming a nearly discharged remote (~2%) as begin state, after 30 minutes, the remote should be charged in the range of 63%. Topping up after that goes a bit slower: in 60 mins, it would be close to 84%. In 2h30m, it could reach 99–100%. Some variation in time may happen, based on age (years) and number of charges. Charging 3 hours is fine, and a few hours longer (e.g. overnight) isn’t bad for the battery either.
Charge the Apple TV remote - Apple TV user guide - Apple Support
↳ How to charge the remote (through computer or AC power adapter recommended)
↳ Check the battery level of the remote (one method only)
It is a small 398 mAh Li-ion battery that charges at less than 5 W.