I'm trying to wonder why the crew of La Sirena would stay together other than they were the show's cast for the first two seasons? Picard wouldn't have had a reason to stay on La Sirena after finding and rescuing Soji. What would Soji do on La Sirena? Same question applies to Jurati, who worked at the Daystrom Institute. I can see Raffi staying on La Sirena with Rios and Seven staying since she didn't have a ship anymore and would want to stay with Raffi. And Elnor would have no place to go. He could've stayed on La Sirena with Raffi, as she would've formed a new surrogate family with her makeshift "spouse" and makeshift "son", but the Academy is the best place for him.
So, in fact, the seven members of the original PIC cast didn't have much reason to stay together. The story of Season 1 organically brought them together. For the story of Season 2, it was more just something they tried to make work.
I think had PIC not returned for a second and third season, they were thinking of having Picard's death at the end of the first season be permanent, so they could end the story if they needed to. Speculation only, but that's why I think they went through with shooting Picard's death and the reactions to it afterwards. They wrote it in before they knew if there would be a second season, and then left it in just in case they wanted to have a storyline about Picard's new body, which they ultimately didn't really do.
When they say they had plans for PIC to be a one-season show, a three-season show, or a five-season show, I can see the case for all three. A one-season show for what I described above, a three-season show in the case of what we're actually getting, and a five-season show, where there would've been a season of story slotted between the actual Season 1 and Season 2 and another season of story slotted between Season 2 and Season 3.