For 2021, you are correct that you will file a Part-Year Resident Return to both California and Pennsylvania if you move to PA mid-year. You report the income earned in each State on their return.
It would be much easier for you if this is broken down on your W-2 for you, if your employer starts withholding PA tax for you when you move. Otherwise, you will need to calculate the amount of income earned in PA yourself, based on number of days lived there vs. total days, etc.
You are correct that you would get a Refund from California, if you pay tax on your entire income there in 2021, filing as a Part-Year resident.
You are also correct that you should owe Pennsylvania, since you paid them no tax on your income earned there. However, PA will give you credit for tax paid to another state, so you may not owe them much (if any). Underpayment Penalties would not apply.
Click this link for more info on How to Allocate Income for a Part Year Resident .
For 2022, if your employer continues to withhold CA tax on your wages, you will need to file two state returns; a Non-Resident return to CA and a Resident return to PA, with the same issue of reporting 'tax paid to another state' on your PA return.
So the ideal situation for you would be to file (and pay for) only one tax return; a PA Resident return with PA taxes withheld on your income.
Hope this info helps you to convince your employer to start withholding PA tax for you (at least by beginning of 2022).
Click this link for more info on Working Remotely for Out of State Employer.
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