Open kitchen without external exhaust recommended? What do you think?

Please explain that again. I did not understand.

If you have a controlled residential ventilation system and a wood stove, you need a pressure monitor according to our chimney sweep. Even if it is a room-air-independent stove (I have read that it can vary from chimney sweep to chimney sweep). If you then turn on the exhaust hood, the pressure monitor triggers an alarm. Unless the controlled residential ventilation is intrinsically safe, then you do not need a pressure monitor and can operate the exhaust hood without any problems.