Can I choose "Not a legal U.S. resident." if I left the US in 2023 July and was not covered for the rest of the year because my employment ended?

Were you on a visa that expired or you went back?  If so, then yes, but are you a resident or non resident alien during the time you were here?  If you were a non resident while here, you would not be able to file through TurboTax, you could use Sprintax.com to help with your 1040NR.