Having had an air source heat pump supplying all my heating and hot water needs, except for the occasional log fire for visual pleasure, for the last 8 years, I would have a different view on some of what you say.
If you want a cold bedroom, then the best way is to use TRVs on the radiators, set the bedroom to a much lower temperature and keep the door shut. That goes whether you heat with oil, gas or heat pump.
Any reading that says expect an X% increase in bills without defining your current usage and housing type / situation is useless as any increase %age will be dependent on your previous use. I live in a bungalow with converted rooms in the roof, 4 bed. It was heated by an oil combi boiler supplemented by a wood burner burning about 3 cubic metres of logs a year although I had a free source for the logs so the value of them in these calls is zero. Cooking was all electric. I worked from home so heated parts of the house all day. My overall fuel costs, everything else staying the same, went down by about £200 a year on installing the heat pump. Savings v gas would be lower (or wiped out) as gas is (was) cheaper to use than oil but I didn’t have that option. At the time I also benefitted from a substantial incentive payment that increased my savings but as that is no longer available I won’t include that in the figures. I also burn less logs, only really using the log burner now for visual pleasure.
Yes, my electric consumption went up but it was offset by the fact I didn’t need to buy in oil. Yes, the way to run the system is different to how you would run a traditional boiler. No you don’t need to run resistance heating for hot water at ruinous costs. I get plenty of usable hot water even in the depths of winter. Only if all 4 of the family want a bath before going out for the evening do I need to run the immersion and that’s because I don’t have a large enough hot water cylinder. I have insulated my house well but then that is sensible in my book however I heat the house. Yes, the install is more expensive than a gas boiler though again that depends on your existing set up. Mine was v expensive but partly because I took the opportunity whilst disrupting the house to undertake a number of other changes to the plumbing runs / hardware etc and they all came in the one bill.
Overall, I am happy with my ashy.
