should Capital loss carryover from 2023 the same for Federal and California State

I just have capital loss (CL) from stock trading all the years and using TT to do my taxes for a long time. No other gain or losses from other sources.

QUESTIONS:

1) running my state tax now, shouldn't my capital loss carryover from 2023 be the same?

2) Why TT said : I have capital loss carryover of $13,800 on my federal return and still asking for my California  CL?  Should it be the same in my case - $13,800? 

Another Questions that I don't really understand:

I fully understand long & short terms  capital gain and loss used in federal calculation. What I don't understand is why that also come up in State taxes? 

1.) Let say, I have $5,000 long term only for 2024  and will pay 15% federal taxes. Do I also pay state taxes for the $5,000 gain?  That is double taxation if yes.

2.) Less say, I have $5,000 long term loss instead, I will be deducting $3,000 of my ordinary income leaving $2,000 carryover to next year.  Does the state filing deduct my state income for the $5,000 loss?

Thanks