Not sure if this goes into bugs or if this is working as intended, sorry!

On their "Defeat Wasps fleet and invade" step, it seems like once you've successfully invaded only selecting "occupy" will complete the quest. Selecting "consume" or whatever their 'raze' option is destroys the 'colony' in the system but doesn't count towards the quest completion, making it impossible to proceed. It's not indicated in the quest text that you need to select 'occupy' in order to fufill the quest objective.

This quest qas written before the Ground Battle rework when there was no option to do anything but occupy. I'll see what can be done about it.