I am being constantly killed by the people at the groundbreaker and I do not know how to make their hostility cease

Unfortunately, I think you'll need to load a save. I think if you kill all the guards, then you should be able to walk around without being attacked, but you might want to switch vendor hubs to Byzantium.

If you don't want to reload a save then try sleeping for some time or going to another place and do some missions.

I think overtime, don't know how long, a faction will not attack on sight. As per hint displayed during loading screen.

 

I'm assuming your reputation isn't 'vilified' by them, so that should be fine.

I got Vilified by Auntie Cleo's and the description says "should be fired, preferably by a cannon" and every single member of that faction starts shooting me. Right now is the only faction that hates me