We know how to do exactly zero of those things.
If you have all of this why would you go to the enormous extra effort to move the habitat to a different solar system? Even if your civilization is so old that the star is a dim brown dwarf that's still plenty of energy for day to day life.
I remember someone pointing out that a generation ship could be problematic because you have one generation who decides to launch this expedition but will never see the end, multiple generations who didn't choose this life and won't get to see the benefits, and then one generation who actually gets to the planet but might not even want to be there. Without some kind of cryogenic sleep or relativistic speeds the whole thing might fall apart just because most of the people involved "didn't sign up for this" but they have to toil away anyway for someone else to benefit from it.
This makes me think of multi-generational migrations north out of Africa. There's only so much that can be passed orally losslessly. Eventually the group in north siberia after 20K years doesn't see living any other way.
That isn't really different from the way things are now. We are, in fact, traveling through the galaxy for many generations and none of us signed up for it. We just happen to be on a largeish ship and have no destination.
That's the point of the AI; it would generally replace that.
Of course, even if we stopped doing that, we'd need to figure out how to visit another place if our ship is passing close by. That also seems to pose a problem: both Voyagers are barely out of the exhaust fumes of our ship's motor, and getting so far took ~40 years.