First off, if it is getting wet around the thermostat housing you should perversely be happy. A much cheaper and easier fix than a head gasket repair.
So it doesn’t look wet in the above picture but with some extra pressure it seems like the the pipe/fitting that goes to the two blocks and contains the thermostat in the middle is getting wet
Small; but, important detail. Not the 'two blocks' but the 'two heads'. The thermostat housing connects to the opening circled in red on the rear head (similar port on the front head). The connection of the housing to the two heads and the water pipe that connects to the pump on the other side of the engine are sealed with O rings.
All of this is above the head gasket level so a leak there can drain down and mimic a leak from other spots. To me nothing appears wet so I can provide no wisdom on the source of the leak.
The fact that the tech at Dilawri is looking above the head gasket level is an encouraging sign. Dilawri's sole NSX tech is methodical. I remember having a coolant flush done by them about 6 years ago. The service department called and said come pick up the car, it will be ready in 20 minutes. When I got there they said oops, still bleeding, here is a loaner car and we will call when it is ready, about 2 hours later. Better to pay extra up front for a methodical diagnosis than jump to the 'its the head gasket' diagnosis.
For some inexplicable reason, the factory service manual specifies that the complete thermostat housing be removed in order to service the thermostat. I am not aware of anybody who has ever done that; but, if some service tech went 'by the book' and removed the thermostat housing to service the thermostat then those three O rings need to be replaced during servicing in addition to the sealing ring on the thermostat itself noted by Honcho. If they did not install new O rings or damaged the new O rings during the install that could be the source of the leak.
Hoping it is a much cheaper O ring replacement that fixes this.