What to do if a wrong chimney has been installed?

The stove has therefore been inspected and works with the fresh air flap open. Where is the problem now?

If means the service flap by flap, not everything is in order. This is not intended for fresh air but for the chimney sweep. It should be closed during operation. An open fireplace door is also not suitable for continuous operation. However, if the stove unexpectedly really has a fresh air flap, it looks different again.

You are right, , the stove must have its own flap. If not, the proposed solution for the builder is to provide a different stove.

you should proceed differently:

A: Only agree on things in writing from now on
B: The builder and/or his bulk materials supplier should offer you a refund because the stove "is not properly operable as installed," it would certainly be possible for you to place a smaller stove where the installed pipe is sufficient.
C: The chimney sweep should provide written proof that the stove works or does not work

You don't have a controlled residential ventilation system (ventilation system), do you?

I am not an expert on fireplaces and stoves. But if the stove is supposed to be operated with supply air through the chimney, it must also have a connection to the chimney, does the stove have this? If not, it is operated with supply air from the room, then I think the draft of your chimney simply does not fit. Which would also explain why it works when opening the service flap.