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”