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The whole point of DC was to have the capital not be part of any state.
And we don't have the concept of city-states.  Because what's to stop NYC, Chicago, LA, Houston, Dallas, etc from wanting the same sized influence. They could each each have 2 Senators and at least 1 rep.
What should happen is DC be cut down to the actual  government section and then the rest ofnthe city be given back to the states that donated the land originally. The population should effectively be zero.
But yes, they should have full representation in sole way.
Carper has led previous efforts to get the bill through in the Senate in partnership with the District of Columbia’s non-voting delegate to the U.S. House, Eleanor Holmes Norton (D), whose name on Twitter is Eleanor “#DCStatehood” Holmes Norton.  

While republicans in the House will never allow this to pass for fear of DC electing Democrats, DC deserves statehood and has for a while. The people there are effectively unrepresented, and DC has a bigger population than Wyoming, which has two Senators! >

You know, I always thought making a city into a state was a dumb idea, but then I learned how populous it is and how empty some states actually are. There really isn’t a good reason not to.