Citation?
I think you just have to live in Georgia and register by December 7. If you moved into Georgia between the November election you can vote in the runoff after voting in your original state.
My fear is all the people who "move" for the election. I expect there will be dozens of new residents at some Atlanta addresses in the next couple of weeks.
https://law.justia.com/constitution/georgia/conart2.html
The runoff is a continuation of the General, so under GA law if you weren’t eligible for the General, you can’t vote in the runoff.
WRT out-of-state people coming in, first see above - the weren’t eligible then and shouldn’t be now. Second, there’s the word of some GA officials (no legal citation) here: https://www.breitbart.com/2020-election/2020/11/13/fact-check-you-really-cant-move-to-georgia-to-vote-in-the-runoffs/