Ultimately it's to claim matter, which is the ultimate limiting factor in how long a civilization lives. For example, you talk about engrossing digital worlds. Well, those worlds require energy and energy means matter.
To be clear we're talking on truly staggering time frames here where a trillion years is a mere blink of an eye [1][2].
Edit: I learned before that this view seems controversial to many people, but I fail to see how on these timescales “humanity” could not be just a transient spark of its own short time.
There is ample reason to believe that any prominent form of life in the galaxy would be expansionary, because otherwise it would be replaced by one that is.
There is no reason to believe that selection stops operating when we are talking about galaxy level scale.
Well, then these hypothetical alien civilizations have barely even begun to start their blink.
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.
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. :)
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".
Gamma ray bursts can probably take out a whole solar system. So could rogue stars or black holes. I think humanity is neat and want it and its descendents to survive until the heat death, so interstellar colonization it is.
But yeah diversification at least 100 light years around in neighboring systems would greatly increase our chances of survival any kind of random brutal event (unless one of our neighbors goes supernova). It will be more of a question of survival rather than 'do we want to colonize that other system'
The cheapest way to fully explore another stellar system is probably colonizing it, so explorers can be manufactured in situ.
And that's all it takes.
Also more source material from real world events could be useful for bootstrapping.
It's possible that will never be interesting to us given the expense, time, and hardships involved.
We have more than enough space and resources in this solar system to support north of a trillion humans if we start building space habitats. So even if we start procreating again after our population is predicted to stabilize, we won't run out of room here very easily.
My feeling is our digital worlds will get so engrossing we will turn our attention inwards rather than outwards. I don't think that lends itself to either population growth or interstellar colonization.
If intelligent civilization is sufficiently rare, that could easily explain the Fermi paradox. They're out there, just too far away and too uninterested in expansion for us to meet.