Finally had the motivation and time to check thing again. The HBV definitely works. I ended up running a straight line from the HVAC vacuum reservoir to the HBV to test it, after connecting the matrix was barely warm and after disconnecting the vacuum it got super hot, the pipes next to the matrix would burn my fingers after a second or two. So the matrix is definitely 100% warm. It was a cheap aftermarket part though so fitment wasn't perfect and it was leaking quite a bit. I used some expanding foam to seal it and ended up realizing that the leaking warm air was the only thing warming up the car lol. When fiddling with the temperature settings I can definitely hear the servo moving and on cold side it's super cold and on the warm side it's probably like 1-5 degrees Celsius. Barely can feel the heat but it does melt the ice from the windshield after 30 minutes.
TLDR: Heater matrix is hot, temperature flap servo moves, but no visual confirmation about what exactly it's doing. Is there a diagram of the hvac system, the flaps? How the servo is connected to the flap. There was a
youtube link in this thread about it but I didn't really understand if it's the correct one. The long plastic handle is the one operating the mixer flap? Because that definitely moves, but whatever it's attached to might not be.