Heat pump vs furnace without rebates

I am in a weird situation where I have a reasonably new AC from the prior owner of the house but the furnace is ancient. It needs to be replaced. I am not sure if I should just install a new high efficiency furnace or replace everything with a heat pump. There are so many conflicting factors

• I have a water boiler, stove and furnace all running on gas while the furnace needs replacement, the others are working totally fine so I don't plan to replace those anytime soon.

• I have heard that while people say heat pumps are efficient, they are more expensive to run than a furnace.

• I don't have solar so installing solar now is not going to happen anytime soon since all the rebates are all gone as well.

What do you recommend I do?