I have a position that the one of the most important technologies needed for interstellar travel (and basically colonizing the entire galaxy) is simply a compact semiconductor fab at a pretty good node -- and it's a technology that almost no one is giving any thought or attention to.

Why do I say so? Because imo the most feasible form of interstellar travel is extremely slow (think a few times Voyager probe speed). Most of the technology (energy, propulsion, etc) to achieve this already exists (unlike proposals like Project Starshot), and you can take huge amounts of mass with you.

The problem is, things break down on your way. Going slow permits bringing large radiation shields (made simply of water), but the time between Star systems would still be of the order 10,000-100,000 years. Not much needs to be done on the way -- hence most circuits and mechanisms can be kept inactive -- but still you're going to have circuits and all sorts of equipment break down. There's a minimum energy expenditure needed for course correction and an associated simple but constant information processing required. So I believe you essentially need to have a way to keep fabricating chips on your way (unless you could store some reserves in a very well shielded compartment?), probably every few hundreds of years. Some elements may need recycling too. Some mechanical components e.g. propulsion systems might need periodic reconstruction/recycling also, but the technology for compact mechanical manufacturing is pretty well established -- a good machine shop with a few CNC mills, maybe some 3D printers and the like can be made to manufacture a complete propulsion system, while also having total self-fabrication capability.

There's also necessity of chips for when arriving at the destination -- again simply bringing the chips with you probably isn't viable, since it would be a while once you could establish a large modern semiconductor manufacturing plant. Again a compact fab is needed (the Starship plant itself could be used in the beginning).

Once you have those kind of capable Starships (which require some difficult but not unthinkable technology), colonizing the galaxy isn't really out of question, provided there are enough Earth-like planets (or other kinds of technologically-feasible planets) out there. You would colonize a planet and use it to build a new Starship once it were well established. Probably needing a few millenia to take over the planet and mine the needed minerals and nuclear fission fuel -- not really a big deal on our colonization time scale of 100,000s of years.

I'm also assuming this is some kind of Generation Ship, because otherwise compact self-fabrication of state of the art semiconductors may be too difficult (one of the amazing things about organic life is its amazing compact self replication). The psychological realities associated with generation ships aren't too rosy, but I think the end goal makes it acceptable (and some engineering can make them not too infernal for their occupants). Plus I find the idea of humans themselves colonizing the Stars more pleasing, but it may well turn out that AI probes will be the ones accomplishing it (if compact state of the art semiconductor fabrication becomes feasible).