We just got 2 new Carrier Infinity 24 heat pumps and I don’t think I’ve ever heard them running (except for the fan pushing air through the ducts, but that’s part of a traditional furnace too). It’s an expensive system that is advertised as being particularly quiet, and I think they deliver - I haven’t noticed any change in noise levels. One of them had an issue for a while so we ran the backup gas furnace instead, and I couldn’t tell the difference between the one that was using the heat pump and the one that was using gas.
So it’s possible to get a quiet heat pump, depending on the model.