According to Wikipedia the latest statehood bill passed by the House did cover this area;
The Washington, D.C. Admission Act would create the state of Washington, Douglass Commonwealth (named after Frederick Douglass), with two Senators and one Representative, and a smaller federal district, known as the "Capital", inside of it. The House would be expanded by one member until the next census reapportionment at which point DC would get the number of representatives determined by their population. The District of Columbia delegate would be repealed. Any residents of the Capital would vote in their state of last residence. The bill would exclude the Capital from the process for counting electors and set up an expedited process for repealing the 23rd Amendment.
The full text of the Resolution is available here, the relevant portions are sections 223 and 224;
SEC. 223. REPEAL OF LAW PROVIDING FOR PARTICIPATION OF SEAT OF GOVERNMENT IN ELECTION OF PRESIDENT AND VICE-PRESIDENT.
SEC. 224. EXPEDITED PROCEDURES FOR CONSIDERATION OF CONSTITUTIONAL AMENDMENT REPEALING 23RD AMENDMENT.
I've trimmed the text of these sections because as is common with government communication the world over they refer to other pieces of legislation without context, but they would hinge on the first section of the 23rd amendment
Section 1. The District constituting the seat of Government of the United States shall appoint in such manner as the Congress may direct:
And essentially make "Congress direct" them not to appoint electors, that would be section 223 of the HR 51 bill until they get around to removing the original amendment via section 224.