Capital gains tax in Georgia

I have a property in Atlanta, Georgia that I am about to sell. I used to live in this house for 5 years until I moved out of state last year. Because this was my principal residence for more than 2 of the last 5 years, my understanding of IRS laws is that I am exempt from capital gains tax.

However, I just got a form from the closing company that they are asking me to fill out which will lead to a withholding of capital gains tax by the state of Georgia. They said it is because I am no longer a Georgia resident.

I did some research online but couldn’t find a definitive answer. This is what I found:
https://dor.georgia.gov/document/form/sales-or-transfers-real-property/download

Q. If a Georgia resident relocates to another state and buys another residence, does his Georgia
residence cease to be his principal residence for purposes of O.C.G.A. Section 48-7-128?

A. In order to be exempt from withholding, the property must be the principal residence of the seller or
transferor for purposes of the income exclusion under the Internal Revenue Code. This rule applies no
matter how much time elapses after the seller relocates to another state. As long as the property qualifies
as a principal residence under the Internal Revenue Code, the exemption from withholding applies for the
gain that is excluded from Federal AGI under the Internal Revenue Code.

Where can I find the conditions under which ‘the property’ qualifies as a principal residence under the Internal Revenue Code? Is it here?
https://www.irs.gov/publications/p523

I filed my 2018 taxes in early January 2019 using my Georgia address and I filed my 2019 taxes in early January 2020 using my out of state address.

I moved out of state for employment and I am currently renting. I bought the Georgia house for cash and am hoping to use the proceeds from the sale of the Georgia house to buy another house for cash.

If Georgia will indeed withhold capital gains tax, will I get it back when I buy another house? Are there reciprocity agreements between states? I know it seems like a dumb question but I am trying to find out every bit of information and leave no stone unturned.