State tax filing

You will actually file as a nonresident in California for 2020.  California advises those who move in or out of California to file as a part-year resident on Form 540 NR.

You will be taxed on your income from California sources.

In regards to your other queries, it will not have an effect on how you file within California.  Your income is from California sources so as long as you continue to work for the same employer based in California, you will still need to file as a nonresident assuming you continue to reside out of the state.