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