Air heat pump new construction manufacturer?

Hello, we are urgently looking for the best manufacturer of air heat pumps. Our base slab for the new building is supposed to be finished next week, now we received a call that district heating is not feasible after all, which was planned, and now we need an air heat pump, but which manufacturer is the best? Urgently seeking advice. Best regards from Saarland

A good start is the Bafa - there is a lot of information and also tables that provide an overview of COPs and manufacturers. Whether there is the best one is another matter... that depends heavily on your heating load. Whether air heat is the best is another question. Have a look in the pink forum ;-) there is a lot to read.

Can you send me a link to it, because otherwise I search for it forever...;)

You meant they enter into a dialogue with the building services? :P

Pink Forum is probably not for me with my limited knowledge ;) They want so many detailed statements... oh... For me, it's primarily about knowing whether an air-water heat pump with solar is to be preferred over district heating, etc....

The following contains many assumptions - the whole thing is just a numerical example - unfortunately, I am not familiar with district heating:

What do you pay per kWh of heat with district heating, what is the basic price? Aren't there also one-time connection fees?

With an air-water heat pump, you pay electricity depending on the annual performance factor. Depending on the size of the house and the design of the heating system, etc., maybe around 6000 kWh - with an annual performance factor of 3, that would be about €45 heating costs per month.
You can ignore solar for now, it's not really worthwhile.