It would almost certainly take an amendment to the constitution to grant DC statehood status.
I'm ignoring the PR part of your post because, while I disagree, it's a matter of opinion.
This is likely true only in that if you give DC statehood, you're going to do it by redefining the federal district to just count for actual government buildings in DC, and if you do
that, you're going to have to repeal the 23rd Amendment giving the federal district 3 Electoral Votes. However, I think in a situation where DC had already gotten statehood, passing a Constitutional Amendment saying that a bunch of federal office buildings don't get 3 Electoral Votes all to themselves would be pretty simple. No one would want that.
