Construction is inflated because the cost of materials have gone way up due to ongoing shipping reductions and factory closures due to Covid. Housing prices are inflated (in places where people want to live) because of long-term bad housing policy and NIMBYism causing slow and the wrong kind of new construction. WFH and eviction bans are likely causing a shift in housing demand.
I wouldn't be surprised if the Fed has some blame. I think there's been a belated reckoning since 2008. But it's a pandemic that has lasted over a year now and there are a bunch of second-order effects out there.