The key obvoius difference between La Sirena and a Starfleet vessel is that it is an ad hoc collection of a task force not a Starfleet or professional vessel, has alot less powers then a Starfleet vessel to deal with problems and Picard(who now has an extra hundred years added to his life) probably doesnt have the desire to become independent from the UFP and fight the Orion syndicate, live of latinum ect . There also needs to be a good reason for the characters to not go there seperate ways. Much of the problems discovered by the Sirena are now in the hands of Starfleet. Thus once Picard returns to his timeline Picard will either split up the Sirena, or find a reason "20 years later"for the crew to reassemble. For Star trek Picard to be transformed into ST La Sirena, with the same crew, it would likely need Picard or recovered Rios to bring coherency to create a crew and then be a courier vessel in the wild frontier of the UFP. Making the La Sirena into a Starfleet vessel would greatly change the DNA of the show which explores vice in the Star trek universe so is unlikely. Thus it would likely take a while for Star Trek Picard to find it's identity post Picard with the nature of La Sirena the defining challenge if the show wants to go for the full 5-7 seasons