In addition to the questions above, this is really odd. If your connection drifts under MCT - this usually happens due to schedule changes, but can also happen when MCT itself changes - then your itinerary is no longer valid. At that point you should be offered options for a new valid itinerary, including rerouting via another airport. It’s nuts that the system didn’t pick this up well before you flew! So in that respect, at least some of the responsibility falls on AA. And if BA let you check in in Cairo and try to make the now very tight and illegal connection then we are really in bizarro world.
Any reimbursement for costs related to the late baggage fall under the responsibility of the last carrier, in this case AA.