I only saw it because Biden badly flubbed it in a speech. It's such a classic example of the government breaking your legs and then selling you crutches.
The President lives in the White House which is in DC but doesn't manage the affairs of DC, although in Biden's case he spends a lot of time in Delaware.
Sometimes Congress will take over the city management of DC if the mayor is arrested for soliciting a hooker or similar.
There is a movement to turn DC and Puerto Rico into states. DC cannot be a state for many reasons, mainly not constitutional.