What items can I claim as my deductions as a gig worker I'm in California
You can find details on what you can claim as a business expense in Chapter 8 of Publication 334 (Tax Guide for Small Business).
As well as in the instructions for Part II of the Schedule C:
Your California (CA) tax return pulls the majority of it's information from your federal tax return. There are some differences in the expenses/deductions you are allowed to claim. CA does not allow you to take the Self-employed health insurance deduction or the Self-employment tax deduction you claim on your federal return and these deductions are adjusted on the Schedule CA as part of your CA tax return.