"Other" Due to infighting, away from the watching eye of Starfleet, there will be tensions and power plays A co-operative will have to be formed, a democracy if you like
Rank or no rank, I can't see the crew accepting Georgiou as captain, especially after what they went through with Lorca. On top of the MU connection, to the degree that is known, there's also her association with Section 31, whom the crew of DISCO have good reason to distrust. They're going to want a captain they can trust, not someone with links to the MU and Section 31. And I like to think that Georgiou is shrewd enough to realize that . . . at least for the time being.
I think that is a terrible idea so hopefully it never does. Accepting the Captaincy from a doubtful Saru or whatever is something Burnham wouldn't do now. She's changed a lot from that brash, ambitious officer we saw in 'The Vulcan Hello'. I think it's more likely that Burnham would help Saru deal with whatever it was that lead him to make a bad call or doubt himself. Saru is Burnham's family now, there is no way she wouldn't try to support him. Also, Saru proved that he is a capable leader even before he went through Va'har'ai.
I dunno who will be, but I think in terms of how the show works, Burnham basically has to be the captain now. Basically the problem is this: SMG is the lead, but Burnham hasn't been the captain. Thus they need to find ways to make her have the most lines in every episode, despite the fact that she isn't technically the final authority figure. The way the series has done this to a large degree is by giving her an extensive backstory and having lots of random stuff happen to her. In the last season there were episodes where her backstory with Spock - even if well scripted and acted - was basically padding to ensure that she maintained a higher line count than Pike or someone else. And even given this, there were still a handful of weird situations where Pike despite outranking her just deferred to her authority when she said something. The problem they have for season 3 is the backstory is gone - or more or less irrelevant. I guess they can string out a quest to reunite with her mama, but all the stuff with Spock, Sarek, Amanda, etc will presumably not matter any longer. The easiest way to ensure she has the lead in lines per episode is to make the buck stop with her character, and the easiest way to do that is by making her sit in the chair.
Even though I think Saru is going to be the Captain in the third season. This post basically sums up what I think... I bolded the key parts of the point you make. It's even stated by Captain Georgiou toward the beginning of "The Vulcan Hello" that they have to talk about her getting her own command someday. That seems to be the only thing left from the beginning of the first season that's still arguably relevant to where they are now. The other being the Spore Drive that's introduced in "Context Is for Kings". The through-line of the series (to me) seems to me to be Burnham's rise from the bottom to the top. No one respected Burnham when she first arrived on Discovery, now everyone is behind her and she's the defacto second-in-command. If that's not a rise, then I don't know what is. If she is second-in-command, then she's back to where she was aboard the Shenzhou. She worked her way all the way back up. And the next step was said by Captain Georgiou in the desert at the beginning of the series.