I think the current context is the Fermi Paradox, so the relevant question is if the AI have any expansionist behaviour after all the biological life dies.

Imagine a version of Star Trek where it turns out that every planet is Risa, only Vulcan is Space Buddhist Risa, Qo’noS is Kinky Risa, Kzin is Furry Risa etc., and all the Vulcans, Klingons, and Kzinti etc. have just been extinct for thousands of years leaving bots behind.