From the Georgia Tax Center website - https://gtc.dor.ga.gov/_/#1
As part of the Department of Revenue effort to protect Georgia taxpayers from tax fraud, the following business practices are in effect for 2023:
I have been waiting OVER 6 weeks for my GA refund. Received my Federal in less than 2 weeks. My employer filed my taxes in GA, which I never lived in 2022. My address was SC. I should have noticed, so my fault. My employer said the software they use should have caught it. Anyway…. My return is SIMPLE. They owe EVERY PENNY I paid to them. I’m getting SO frustrated. When I called, was told “we’re short staffed. Call back when it’s been 90 days.” So, do they owe me for 1 1/2 years they’ve been using MY money that was never theirs to begin with?!?! I’m sure I would be paying interest if I OWED them that money.
All you can do is wait for the refund since neither you or the employer did not notice the incorrect state withholdings were being taken earlier. No amount of complaining here or to the state will get them to process your return any faster. Their own web site says it will take 12 weeks or more.