Should I file my state extension in California if I already filed the e-filed federal extension?

yes, you should file the State of California extension.  These are two different tax entities and CA would have no way of knowing you filed a federal extension.  Better to be safe than sorry..

If you’re planning on mailing in your taxes to the state of CA past the midnight deadline PST on May 17, 2021 then you probably should file an extension for CA.

If you mail it before the deadline for CA then no.

You can also file your CA state taxes for free here, using your Federal taxes as your guideline.  I believe it’s pretty easy.
https://www.ftb.ca.gov/file/ways-to-file/online/calfile/index.asp

I found this information in the California website:

California grants you an automatic extension to file your state tax return. No form is required. You must file by October 15, 2021. Your payment is still due by May 17, 2021.