If I lived abroad for 6 months out of the year as a Fulbright Scholar but still maintained a residence in GA, where do I add this info?

If GA is still your domicile (your main, primary home, to which you intend to return), and your stay abroad is temporary, then for state tax purposes you remain a full-year resident of GA.  In the Personal Info section of TT, you would enter GA as your State of Residence.  The mailing address on your tax return should be the address you want the IRS and your state to use in case they need to contact you.  (Those contacts are done by regular mail.)

As long as you are domiciled in GA ALL your income remains taxable by GA, regardless of its source.

You may want to review this IRS tax reference regarding taxation of U.S. citizens living abroad:

https://www.irs.gov/individuals/international-taxpayers/us-citizens-and-residents-abroad-filing-requirements#:~:text=If%20you%20are%20a%20U.S.,residing%20in%20the%20United%20States.