CA & PA State filing

You should have 2 part-year returns for California and Pennsylvania.

In the "My Info" section of TurboTax, confirm that you have entered the correct state information:

1. Click "Edit" to the right of your name
2. Confirm your input under #2 "Tell us the state(s) you lived in"
3. Confirm the rest of the state-specific questions here as well including the "previous state of residence" and "date you became a resident" of the state noted
4. Do the same for your spouse if you are married filing jointly.
5. Go back to the personal information section, and verify the mailing address and "Other state income" section.

Review your input on your W-2 Wages under the "Income & Expenses" section.

Confirm that you have entered the correct state for each W-2 in Boxes 14-15.

Next, prepare the state return for the state which you are no longer a resident of.

Then prepare the state return for the state where you lived at the end of the year.

Each state has a different set of questions you need to answer as you go through the interview section.  Be sure to answer each question carefully.  

Since you mentioned not having any withholdings in PA, you may want to contact your employer to confirm that for 2020, they are withholding taxes in your resident state.

You are correct in stating you may owe taxes to Pennsylvania.  I would recommend completing the section in PA which allows you to take a credit for taxes paid in another state.  It is possible all of your wages were taxed as if you lived in California for the entire year.