You shouldn't spend that much. If you need an air conditioning system, making it a bidirectional heat pump is negligible unless people are trying to rip you off. (They are)
Comparing a cold-climate AC to a cold climate heat pump shows how confused YOU are.
ACs in cold climates are cheap. Cooling a house down 20 degrees doesnt take a lot of BTUs. Plus they’re just cheaper per-BTU and a typical northeast homeowner is going to be comfortable installing a cheap brand because it’s not life-or-death if your AC goes out.
When you start talking about having a heat pump being the primary heat source in a cold climate home, that’s a different ball game. First you need WAY more BTUs to heat a house in winter lows — even NYC hits single-digits most winters, that’s a 60 degree temperature differential. And you need to be prepared for the worst temperatures which basically necessitates a top-end brand like Mitsubishi which is rated down to historic-ish lows.
Not to mention that many homes don’t have central ducts, so converting to a heat pump means ductwork or mini splits..
No, the difference in cost between central air conditioning (a heat pump that works in one direction) and a heat pump that works in both directions is negligable unless you're being ripped off.
Here’s a concrete example that took 5 minutes to find. Two condensers from the same company, same seller, same SEER, same series, same tonnage, except the second does heat. The heat pump is 29% more expensive.
2 Ton 14.3 SEER2 Trane Air Conditioner Condenser - RT Series. $1615