You could always borrow a laser hygrometer to check humidity levels.
Is there a thermal break between the walls and the metal studs where the pipes are going to run? Personally, I'd put rubber pipe insulation on the pex and not worry about it. As Endo1030, it's a conditioned space.
There is 1/2" between the studs and the concrete wall.
Are you saying you wouldn't worry about the pex freezing or wouldn't worry about putting up a vapor barrier?
What you have is XPS rigid foam in a conditioned basement. At 2” thick and taped it qualifies a a vapor retarder with a Perm of ~0.5. The poured walls will continue to dry out, albeit at a very low rate (and thats fine, provided they were done right in the first place).
For comparison, 1/2” gypsum with 2 coats of latex paint has a Perm = 5, or an order of magnitude greater, so moisture that eventually migrates from your walls through the XPS will have a much easier time permeating through into your basement. Which is what you want (your wall cavity will not become a humidity trap).
I don’t see any reason for further concern here. You’ve got a vapor retarder on the inside portion of your foundation walls, and a thermal break (gap) between the metal framing and the insulation. Just don’t go off and install another several inches of insulation on the basement side of the framing, as that could prohibit the wall’s ability to dry out and make the wall cavity colder (by blocking heat transfer from your conditions space - aka the basement - into the wall cavity)
Why did you use metal framing? Just curious...