I work for a company in Florida and a resident of Georgia. Can I get any penalty for paying my state taxes together for a year?

Q.  Is there any tax advice to lower the state taxes for GA?

A. No.  Since you work in a state without an income tax, your resident state taxes all your salary. If you worked in a state with an income tax, your resident state would give you a credit for any tax paid to the work location state.

Q. Do I get any penalty for not paying my GA taxes monthly?

A. Yes, it's called an underpayment penalty.  If your employer is unwilling/unable to withhold GA tax, you should make quarterly estimated payments to GA.

TurboTax (TT) can prepare the quarterly payment vouchers. In your 2023 GA software, enter at Other forms/Estimated tax payments for next year.

 If your goal is just to avoid the underpayment penalty, then paying 100% of the prior year tax liability is the “safe haven”