I see two major dynamics that could drive interstellar colonization:
1) Eccentricity and Boredom: I think that with a solar system population in the trillions, you will inevitably have a sufficient population of eccentrics to eventually launch generational ships. This is especially likely if humanity survivea long enough for the lifetime our own sun to present a realistic limit on the survival of the species.
2) Eccentricity and Freedom: The major advantage of interstellar colonization is distance from dominant power structures in the solar sytem. I find it quite possible that there could be societies that view fleeing the solar system as their only path to survival as a cultural unit.
One of the interesting consequences of interstellar colonization in a universe without FTL travel or communication (which, by all indications, appears to be our universe) is the sheer amount of cultural diversity it would create. Even adjacent systems would have communications round-trip times on the order of single-digit years, and depending how far apart desirable systems for colonization are it could even conceivably be decades of round-trip comms lag to the nearest inhabited system. Centralization becomes impossible, and star systems would have only very weak cultural impact on their neighbors.
Not just cultural but also possibly biological/corporeal diversity as the different cultrues start to adapt to their specific local environments.
The Orions Arm collaborarive hard SF universe has very many first contacts due to this as as often two civilisations of human origin that meet each other look to each other totally alien (one can survive in liquid methane, the other near stars in hard vacuum). They did meet a few actual (and very unique) aliens but it took a lot of verification it's not just another hyper adapted modification happy ofshoot of humanity. :)
Interstellar trade of physical goods is quite impractical without FTL. If there is interstellar travel for non-colonization purposes it seems like the primary goal would be to enable low-latency communication to compensate for semantic/cultural drift that could interfere with the efficacy of the high latency communcations.
It seems to me that interstellar trade -- with or without FTL -- is quite unlikely. I wrote some thoughts on this about a year ago, (https://one.mikro2nd.net/2021/07/interstellar/) but tl;dr: If your society is capable of marshalling the resources/energy necessary for interstellar travel in the first place, you have most likely, of necessity, solved the problem of getting more resources. War seems slightly more likely because "ideology".
Ultimately I think my notion is quite similar to yours: that the primary exchanges would be culture (art, music, fashions, language, rites,...) so the things for which we want "communication".
1) Eccentricity and Boredom: I think that with a solar system population in the trillions, you will inevitably have a sufficient population of eccentrics to eventually launch generational ships. This is especially likely if humanity survivea long enough for the lifetime our own sun to present a realistic limit on the survival of the species.
2) Eccentricity and Freedom: The major advantage of interstellar colonization is distance from dominant power structures in the solar sytem. I find it quite possible that there could be societies that view fleeing the solar system as their only path to survival as a cultural unit.