The key here is two-fold. First is the cost. Was it less than $2,500? (that includes the cost of labor.) If so, then it was to replace an existing asset, as opposed to installing a new asset? So if you replaced the heat pump, and not the entire system (which would include the whole outside unit and the whole inside unit) then it's a repair expense if it was under $2,500. I'm sure it was well under that price too.
Whereas replacing the entire system would easily exceed $5K and that would be a property improvement hands down.
What you have (if I'm interpreting your post correctly) is a repair expense because you replaced the heat pump only to keep the entire system working.
Now if you're calling the entire outside unit the heat pump, I know you paid more than $2,500 for it, including labor. So that would be a property improvement.
