Problem
New House build, Builder & subs top rated
Humidity levels tweaked by HVAC guys but .... still
water condensing and dripping out of the vent hood above the stove

It's not the damper nor the 6-in flue ....

Going to advise HVAC supply air from vent be directed away from the hood but know already these top HVAC guys would have done that on this repeat visit .... ugh

Update Aug 22: GE Range Hood UVC9300SL1SS
Vents up then through floor joists to exterior wall, cheap alum exhaust/flapper near roof/rain splash & HVAC 5ft away & below
Int. HVAC register 6x10 small side blows toward hood 6ft away

Exterior vent, is it catching a bunch of wind and blowing back into house causing build up in hood? If it doesn't have one, put on an auto closing flap vent to help with that. There are flat ones and ones with a hood covering the entire vent with a recessed flap to help stop wind.

many times based on direction of the facet the vent on the roof is on, wind driven rain can cause drips on a stove. This is one of those rare things that happens. Vent style would just need to be changed out.

If it is condensation, they might need to insulate the pipe all the way to the roof deck.

Had this happen to the bathroom vent after a big storm. I found piece of scrap sheet metal and bent it to form a type of extended shield over the existing vent, sort of like "shading" the opening. Attached with self-taping screws. Never had water enter the vent again. The flap idea is the ideal way to go, but I opted for the DIY solution to start with, and it worked.