I've tried to make the idea work in my head many times but my conclusion has been that I don't think there's quite enough co-incident demand for heating and cooling in the average house. For example, yes, I could generate all my domestic hot water from heat from air conditioning in summer, but in winter I need to be able to generate it plus heat the house, so I need enough capacity to generate that heat from the outside air when I'm not using air conditioning (so I don't save on not needing as much capacity), and the efficiency gains probably aren't worth the extra complexity.
For applications like commercial buildings, public swimming pools, industrial sites, etc. can (and increasingly do) definitely benefit from that kind of combination though.
I think the big issue is the different "tuning" for each heat pump system. For example, a heat pump water heater needs a different maximum temperature than an air conditioner, and has much different cycling behavior. This leads to very different design decisions, including refrigerant choice, pressure, compressor type, whether the refrigerant loop is even serviceable, etc. (Some appliances operate at a refrigerant pressure so high that they require being fully assembled at the factory, which would be a non-starter for a manifold system like we're discussing.)
I think this might eventually become a thing once science gets us far enough that there's an "obvious" refrigerant choice for most applications, but we definitely aren't there yet. There are hundreds of different kinds that perform better or worse in different applications.
AFAIK all of the big commercial systems that do multiple different types of heat transfer use water to do it, thus bypassing the entire refrigerant selection issue. Right now the most advanced we can do is VRF ("Variable Refrigerant Flow") systems that can individually select air handlers for cooling or heating (i.e. move the heat from one room to another). These are still commercial units and not really available for residential installs.
There’s a reason new houses get built with geo based heat pumps in Finland.
This enables your hot water heater to use the same circuit to heat water - that decreases your hot water bill to around a third, even in winter as the necessary heat isn’t taken from the indoor air but from the ground.
For applications like commercial buildings, public swimming pools, industrial sites, etc. can (and increasingly do) definitely benefit from that kind of combination though.