The original plan was to have each story be a season long, have it be an anthology with a different crew, and they would go from the TOS Era to the TNG Era and then to The Future. Looks like they've bypassed the TNG Era and shot straight for The Future instead.
Once the idea of switching ships and crews every season was vetoed, so too went out whatever the "original plan" was. I'm going to guess the Spore Drive would've been the through-line on the show. It would be developed and abandoned in the TOS Era, research on it would pick up again post-NEM, and who knows about The Future.
I remember, during the first season, they said it would be eventually explained how DSC links up to TOS. That was probably thought up after Bryan Fuller left and fan concerns started coming in. If it was decided to address it, but still stick with the same ship and crew, then it makes sense to assume they didn't want to cram all that into the first season, and saved it for the second.
So I'm guessing from the third season on, DSC will be the show Michelle Paradise inherited, that's already been taken out of the TOS Era, and she'll be able to develop essentially a revamped series around the USS Discovery, who's left on the ship, and whoever is in the 33rd Century.
The fact that Michael Burnham has Gabrielle Burnham possibly waiting for her in The Future means that Burnham will be interacting with her biological family again, instead of her foster family, which means that we'll see a Burnham without any type of connection to Spock's Family. It re-frames her character.
The time-setting really changes a lot. It fundamentally alters the show. All you have left are the characters, free from the setting they originated from, so we get to see them outside of that context. And having one showrunner from start to finish will make a difference too.
Pike's thumbnail description of each of the bridge crew when he said goodbye in "Such Sweet Sorrow", in an episode where Michelle Paradise also has writing credit, was probably her way of leaving a rough thumbnail of who these characters will be that she develops in the third season. Because very little was done with the bridge crew during the first two seasons, she can put more of her stamp on them than she can with Burnham, Saru, Tilly, Stamets, Culber, and Georgiou.
Tying back to the original topic of what I thought about Season 2 overall, I think that it was a transition season from Old Disco to New Disco. Both within the story itself and unintentionally behind-the-scenes. Who knows what Old Disco would've turned out to be like. New Disco can forge its own path without having to work around what someone else had in mind or addressing uproars about it being a prequel. I think the overall thrust -- that eventually came to be -- was Alex Kurtzman and Michelle Paradise wanted to get to the point where they had their own show instead of just something they inherited from Bryan Fuller, Aaron Harberts, and Gretchen Berg. Now they have it. Let's see what they do with it.
