We do have to remember that "Captain" aka "retired Captain" was only ever her alias, not her identity.
Although it's also a perfectly good police rank, very different from either Navy or Army Captain... And it's lower than Commander in a police organization, so Georgiou's latest form of address could be considered a promotion.
What I'm the most interested in is whether Georgiou still holds her status as S31 employee. I mean, barring behind-the-scenes machinations, she's just as entitled to that as Saru is to thinking of himself as a Starfleet officer. The practical implication would be that the Emperor could then quote regulations entitling Starfleet Intelligence to walk over regular Starfleet operations in appropriate situations...
Timo Saloniemi
Sure, Section 31's structure could be completely separate from Starfleet, but that's not the picture that season 2 of Discovery painted. It appeared that Section 31 was widely known by Starfleet officers and almost as if Pike and Leland had known one another as Starfleet cadets. We know from DS9 and ENT that at least some Section 31 agents were simultaneously Starfleet officers: e.g. Bashir and Reed. The ranks could be separate, but unlike the Bajoran Militia in DS9, the writers thus far have made no attempts to signal that to us, which if that's what they intended, would have been helpful to do.
Regarding Mirror Georgiou, prime universe status, everything was predicated on the idea that she had in fact taken on the identity, rights and privileges of her prime counterpart: her rank, reputation and social location... and that her true identity as a doppelganger was top secret outside of the Discovery crew and the highest officials. That means, on the face of it, if they call her "Captain" its because she is a Starfleet captain. A retired captain is still a captain. And she could hypothetically pull rank on Commander Suru. Commanders cannot make themselves captains. In order for this to be coherent, Admiral Cornwell had to have authorized this course of action before they left. Besides, as with naval tradtion and exaemplified in DS9, those with the rank of "commander" can also be assigned as "commanding officers" of starships and space stations.
I agree that Georgiou has as much right to her status as a Section 31 agent as Suru has to calling himself a Starfleet officer. But we do not know if Section 31 still even exists. What will be interesting will be how future-present Starfleet will receive all of them once they are undoubtedly united. Since we have seen them wearing a new badge, it's safe to assume that they will eventually be embraced.
Lastly, I am actually excited to hear that photographed one-to-one conversation between Saru and Georgiou in the ready room.