if my group has been spilt up, and they are both researching using engineering. If group 1 has a breakthrough, which then stops the group using the trait for the rest of the adventure, does it also stop group 2 using engineering to do some research, and if not, what happens when the 2 groups join back up?
I'd say that group 1 can't use that trait anymore, group still can. If you ever join the two groups, they both can't use that trait anymore.
That's how I would play it.