Had the event, sent the ship to an area (as the Unfallen/tree people?) immediately colonised it and then a few turns later it failed. - there was plenty of space, I just did things in an order the game was not expecting

The ship stayed behind and I got to keep it, this might be as designed or another bug. If a bug, I think it happend because I docked it into the system.

I got that quest too, moved the ship to a system A, colonize it and nothing happen, moved the ship to another syst B and back to A, quest OK 

It seems to trigger only on entering system.

And yes the ship remain in game after.