If the employee quits, the 72 hour-rule should give you plenty of time to contact HR/Payroll to calculate wages, tips, taxes, unused PTO, etc. on the employee’s final paycheck. There should be no problem here.

If you are firing the employee, you need to have the final paycheck w/ all calculations listed above ready at termination.

In my personal experience, you should fire them the next time they come in, but before they start work (I think it was minimum 2 hours pay, or half the time they were scheduled for, whichever is greater, but I could be wrong) with the unworked hours just given away as free pay. Firing them at the end of a shift causes problems because you can’t calculate tips on a final paycheck that quickly unless you have payroll on call 24/7 or the owner is doing it themselves in an on-site office lol.

Assuming you gave sufficient notice on California law to be paid on your last day then yes your employer is obligated even if you didn't ask for it. There is no exceptions under the law to being paid on your last day except with insufficient notice.

Generally, I would contact your employer to collect it before filing a wage claim. If you can get a check cut, even if it means showing up in person, as that will be the fastest way.

Even though you are due that money. A particularly asshole might decide to let the wage claim process play out, thus delaying your final paycheck for months as it plays out. The penalty in California for failing to pay the last paycheck on time is a day of pay for up to 30 days. Obviously, your employer will refuse to pay the current penalty already accrued. So the only way you get that penalty is filing the wage claim and waiting those many months.