Connecting/controlling BLE thermostat out of range - multiple instances?

I’m running Home Assistant on Raspbian (not on a Raspberry Pi Zero W positioned approximately in the center of my apartment. I also have several eq3bt BLE thermostats around the house, one of which is out of Bluetooth range from the Raspberry Pi.

I originally wanted to install another HA instance on another Raspberry Pi Zero W to control that one thermostat (and maybe others in range), and connect that instance to my main instance, but it seems this setup is deprecated.

Has anyone faced (and solved?) a similar challenge? I’m grateful for any pointers what the best setup would be for this. I want to be able to read and control the temperature of one eq3bt thermostat, but ideally without manually configuring each device.