The angle I’d use to start from is “What differences would having X% of the population achieve a conditional form of reincarnation/immortality lead to for Trill culture and arts?”
Well, the oral tradition of prewritten history would probably be better preserved than ours, due to less links in the telephone chain. But otherwise, my guess is cultural drift would account for most of it. Lots of identity pondering, but humans have got that already.
But there is one thing. The first host picks a theme. Idea. Musical motif. Whatever best fits their talents, and they do an art about it. The second host revisits the theme, perhaps not within the same medium, and treats it to their own take. The third, the fourth… etc. etc.
Hundreds of years later, and an anthology builds itself like sedimentary layers. A single theme running through to unify it, but each piece is distinct enough that you can sense the individualities who existed, and you can understand how they feed into each other in an unbroken chain. How the effort grows more full and more complex with each lifetime.
I suppose, depending on the timeframe, one way to bring Jadzia’s family into it would be to have them checking out the Dax collection, and trying to use it to feel a connection with Jadzia’s new self.