Since downspouts aren't an issue ... I doubt the condensation from all the copper pipes would provide enough moisture to do what I see.
The sump pit is dry, so my guess would be that ground water is sitting in the dirt of the crawl and making the whole thing damp.
Maybe they didn't put a sock around the drainpipe, maybe it's clogged up or maybe it's not even there. I'd suggest they get a camera guy in there to look into the drain pipe coming into the pit.
I'm still wondering why the pipe froze.
You are wearing a mask when you go into those crawls, right?
How's the exterior grading at front and rear?
No downspouts on the front or rear seems a bit odd also.

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