You’ve shifted and redefined the goalposts and even then requires orders of magnitude advancement in multiple areas (power generation, lasers, satellite shrinkage etc) and doing it all in space. Thinking any of this happens in a lifetime of anyone alive today seems unrealistically optimistic. And all of this ignores something critical OP said:

> we'll expect people to live hundreds of years by the time we can send a ship to alpha centauri.

Even hundreds of years is not a realistic life expectancy to reach the nearest star and requires not just an enormous overabundance of energy, the fuel source has to be available at the midway point so that you can decelerate. Humans at another star without discovery of faster than light travel mechanisms (mainly wormholes) seems purely in the realm of science fiction.