Still, this is many, many orders of magnitude short of what’s being discussed. Essentially the forefront of technology could get us to just barely speed past our nearest neighbor in one human lifespan.

That's why we need to find a globular cluster with metal-rich planets, and take a generation ship over there.

Sure, a thousand generations will live and die along the way, but once we get over there, you've got stars every 0.1 ly or so, and with very plausible future tech, you could navigate between them in a few years. You could set up a proper starfaring, interplanetary civilization, with tradeships either going back and forth between two neighboring systems, or winding on long, never-repeating routes, visiting a dozen or so star systems in a human life.

(Most globular clusters appear to be old and metal-poor, and we haven't found a lot of planets there, and this only works if you find a globular cluster where ~every star can support a colony.)