I quit my job on 6-4-23. How should I report the change on my return?

Job changes are not reported on a tax return.  If you were a W-2 wage employee you will receive a W-2 from the job that you quit in January 2024.  Make sure that they have your current address since the W-2 will be mailed to you.  If you are a W-2 wage employee on your new job you will also receive a W-2 from them in January 2024.  Both of the W-2's that you receive are reported on your 2023 tax return that you will file in 2024.

there is nothing to report other than reporting BOTH W-2s on your tax return early next year

Make sure the old employer has your current address if you moved so the W-2 gets mailed to you next January.