Can I increase my Fed refund and reduce my CA Due by applying for a home solar tax credit ?

Maybe.  If you installed solar in 2023, you should definitely explore that possibility.

When you purchase solar equipment for your home and have tax liability, you generally can claim a solar tax credit to lower your tax bill. The Residential Clean Energy Credit is non-refundable, meaning that it can offset your income tax liability dollar-for-dollar, but any excess credit won’t be refunded. 

If the credit exceeds your tax liability for the year, you can “roll over” the unused portion to future years so long as the credit remains in effect.

There are no income limits on the solar tax credit, so all individual taxpayers are eligible to claim the credit on qualifying solar energy equipment investments made to their homes within the United States.

Here's detailed info on Federal Tax Credit for Residential Solar Energy.