Where do you live? The trees in your yard look like the ones we have here in western West Palm Beach, FL. I don't know how clever bobcats are about getting into coops like yours (which looks fantastic, by the way!) I have had problems with bobcats stalking & catching my ducks & chickens on the ground, on the fences, and while roosting up in trees. But I don't know if they could/would try to squeeze into a fenced coop.
I think you could keep your flock safe in there by making sure all the edges of the wire were securely battened, adding a couple of electrified wires around the coop, and also keeping your chickens securely closed in their little house overnight.