We can reasonably send something to Alpha Centauri in 100 years assuming you can get the drive to work, but that’s the closest star to us, and Project Longshot was a design for an unmanned probe.

Yes, the British Interplanetary Society did do a study on what a manned mission might be like, but they always seem to underestimate the biological problems of space flight.

If you wanted to colonise a planet around a nearby star it would be a truly staggering undertaking, even getting the fuel for an unmanned probe probably require H3 mining of Jupiter.