At the HVAC control level it would be a Pico - for the development / maintenance time efficiency: I know how the tools work, I know the community support is there, the hardware is easy to find and available relatively reliably, although ESPHome on the ESP micro-controllers is pretty good too.
A RPi is going to be smaller, quieter, and 10x more energy efficient though…
There are probably a dozen things you can do to save energy on orders of magnitude higher than using a pi.
Then do them. It’s still not going to decrease the energy use of your server.
Like: using the pi to manage your HVAC more efficiently.
Why use a pi instead of a microcontroller?
At the HVAC control level it would be a Pico - for the development / maintenance time efficiency: I know how the tools work, I know the community support is there, the hardware is easy to find and available relatively reliably, although ESPHome on the ESP micro-controllers is pretty good too.