Fortunately, any state of the art ship with ChatGPT on board will quickly get passed by the state of the art ship of a decade later, with a decade better AI too.
The universe really doesn't want ChatGPT!
It is fair to say, that given space travel tech improves slowly relative to AI, but the distance to be travelled is so great that any rocketry (or other means) improvements will quickly pass previous launches, the first intelligence from Earth that makes it to another system will be superintelligence many orders of magnitude smarter than we can probably imagine.
Space ship speeds are unlikely to keep ever increasing. In the limit you can’t do much better than turning part of the ships mass into energy optimally, eg via antimatter annihilation or Hawking radiation, unless you already have infrastructure in place to transfer energy to the ship that is not part of the ship’s mass, eg lots of lasers.