How to improve Homekit range from an Apple TV ?

not sure about what homekit enabled devices you use and how they connect but all mine connect to my wifi network which is how they communicate with the appletv so extending the network would be a thing for me if they were out of range, not to purchase another appletv

You might want to think about another wifi access point. If it supports it you could possibly use it as a wifi repeater but depending on how much traffic the ancillary devices create this might be problematic as repeaters will reduce network (although I can't see it as much of an issue for a window sensor, myself) The other option would be to extend the network using plugged into the additional access point which you then use as a remote access point with it's connection details.

EDIT, agh, forget that if it's BT.