What is your model remote? Identify your Apple TV remote - Apple Support
Remote firmware is model dependent (each model may have a different current version), and could be included with select tvOS updates. It updates automatically (no manual options), at a moment when Apple TV and the remote are both idle. (It is probably a good idea to keep the battery charge level above 50% once in a while, as that is needed for automatic updates on some other Apple devices.)
The current version for the 2021 model Siri Remote (2nd generation) seems to be 0x0070 from 2022-07.
The current version for the 2017 model Siri Remote (1st generation, white ring) seems to be 0x0118 from 2020-01.
I do not have access to other models remote to check.
I don’t think the operating distance is influenced through firmware.
See: If your Siri Remote or Apple TV Remote isn't working - Apple Support
Or possibly there may be sources of bluetooth interference in the vicinity? Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support