If the final goal is of local scope, energy acquisition from out-of-system seems to be mostly irrelevant, considering the delays of space travel and the fast time-scales a strong AI seems likely to operate at. (That is, assuming no FTL and the like.)

Do you have any plausible scenario in mind where an AI would be powerful enough to colonize the universe, but do it because it needs energy for doing something inside its system of origin?

I might see one perhaps extending to a few neighboring systems in a very dense cluster for some strange reason, but I can’t imagine likely final goals (again, for its birth star-system) that it would need to spend hundreds of millenia even to take over a single galaxy, let alone leave it. (Which is of course no proof there isn’t; my question above wasn’t rhethorical.)

I can imagine unlikely accidents causing some sort of papercliper-scenario, and maybe vanishingly rare cases where two or more AIs manage to fight each other over long periods of time, but it’s not obvious to me why this class of scenarios should be assigned a lot of probability mass in aggregate.