Technology

I suspect the reasoning here is going to not be obvious so some people so I'll add a little. Heat pumps are more efficient when there's a larger difference between where they're getting heat and where they're putting it. I'm going to call this difference a gradient, because otherwise later I'll be saying "differences of differences" which gets confusing. The argument here is that moving heat from compartmentalized 90 degrees server room to outside at 95 degrees with a separate system for the house, moving from 75 degrees to 95 degrees, would be more efficient than a single heat pump moving air from the mixed rooms at 80 degrees to 95 outside.

The magnitude of that effect would depend on how nonlinear the relationship between efficiency and the gradient is. I'm not very familiar with that. I assume it's nonlinear, but whether it's highly nonlinear from a gradient of 5 to a gradient of 20. From here, it's quite nonlinear from a gradient of 25 to 40, but from 5 to 20 it's pretty linear: https://www.ecosia.org/images?q=heat%20pump%20effeciecy%20vs%20temperature%20gradient#id=598B80C1EB5A721C392964CB7708512FC496B78F

This also doesn't consider that these are operated with thermostats. Presumably someone is going to set all of the thermostats to the same temperature, 75 degrees or whatever the preference is. The gradient at which the pumps start will be the same in all cases, and the difference will be in how often the pumps run. There will differences in the average efficiency because of the time difference, but it's by no means obvious to me that there would be a significant benefit for a typical home. I would want some clear evidence before spending money on this.

Edit: I said they're more efficient when there's a larger gradient, but I should have said the efficiency depends on the size and direction of the gradient. When the gradient is positive, it's less effecient. Overall, the conclusion is the same. It's dubious that, for this case, using two heat pumps with compartmentalized rooms provides a tangible benefit over a single pump with mixing.