How much ventilation is needed here?

Thanks! I tried my best but couldn't get it to insert the image on mobile.

Yeah the ceiling joists for the patio are hanging off the rafter tails from the house. Each joist has 6 framing nails holding it to the rafter. They don't go through the sheathing. They appear to be holding up a central tie and vertical support, but they're only about 7'6" off the ground. He wants to put the ceiling up above the joists and hang it from the rafters holding up the patio roof, which run parallel to the house. It's pole-barn style, so the tension load is handled by a big treated LVL beam on the exterior gable edge of the patio directly behind me as I take the picture. This top, triangular section of the wall is what he added himself. He built a frame out of PT furring strips and secured it to a porch rafter at the top and the face of the house at the bottom, then nailed primed 3/8 ply that matches his original siding over it.

Behind this new wall is about 150 cubic feet of open space, shaped like a triangular pyramid with the flat face towards you and the "tip" the farthest point away. One face is the old roof of the house, which was left in place when the patio roof was built. The new structure was bolted right through the old roof, then flashed and reshingled to make a continuous roof. That old, now enclosed roof is the roof over his living room, which has a peaked ceiling. The only thing between the sheetrock and the decking is 2x10s and whatever insulation is left from 1989 when the house was built. I'm concerned that the old roof will provide a cool surface (since it's so close to AC) for humidity (Houston area) to condensate on and cause moisture intrusion problems down the line. I'm wondering if cutting 6 or 8 4" round holes in it with a hole saw, stapling screen over the holes, then trimming them out to look half-decent will provide enough airflow to prevent moisture build-up, or if he'll need to go a little more elaborate and "force" some air exchange using a small exhaust fan.

Cut in a couple of 6" return grilles. Paint them the same color as his trim (or leave them white if trim is white. Put some black bug screen behind the grille to keep birds/bugs out.

Assuming he has a traditional Unconditioned attic, this would act just like soffit vents did on his old roof line.

No need to insulate if the space behind that wall top out is un conditioned.

Did he put a vapor barrier behind the sheathing? If so, and everything is properly sealed and flashed, I would leave it as is. If not, maybe install a couple of small louvered gable vents with a bird/insect screen. Make them removable and you will have some access to the small dead space.

Based on your description, venting this area might only change the location of the surface where dew point conditions occur to the old roof, which has now likely been compromised by the over framing.

Why not just remove the paneling above the ceiling joists?