I haven't looked at the contract in detail, but no, $3B over 5 years for 3000 people including construction costs sounds reasonably in line with prison costs (the closest comparison). Certainly not the order of magnitude too high like you're suggesting, which surely someone would have undercut on the bid if it were easy.

You can look at the bid requirements yourself and determine whether you think it's reasonable for the scope of the facility: https://sam.gov/opp/3726d9e2246c47e197396e805ce6bb33/view

This was awarded sole source. There were no vendors able to compete.

I also find their J&A unconvincing, and there's no way it passes the smell test required in Far part 6.

There was really no other vendor in the world, besides Family Care to be able to do this? They aren't even a construction company.