I hear you. But some of that thinking is recent bias.I would disagree slightly here.
For Georgia
1) Florida
2) Florida
3) nothing much mattering other than Florida losing
next varies a little based on year(s).
Georgia really does not spend much time thinking about GA tech, where I feel all GA tech does is think about their hatred for UGA.
Auburn/TN: Georgia fans as a whole do not like these two teams.
South Carolina was a big rival when Spurrier was the coach, not so much anymore
Many Georgia fans would put Bama near the top of the list these days, but simply because Bama has had Georgia's number and obviously Bama is a standard that Georgia wants to be.
Me, I have respect for Bama as I feel the rivals are similar (Auburn and TN near top of list) and both teams are currently operating at a higher caliber of recruitment and season winnings.
I definitely put Florida first. Clearly it is. And your feeling toward GT is similar to Alabama’s toward Auburn. But it is definitely the next historical rival.
Just like some here mentioning LSU or Georgia for Alabama. That is ridiculous. It is Tennessee and Auburn in whatever order you like and that is it.