I am dealing with lost luggage right now with AA / BA as well (BA lost my bags on an AA ticket at LHR)... The only thing I can say to you is that for future reference, it's very helpful to put an Apple Airtag in your luggage...

While I'm not happy about missing my bag for 5 days now, I do know that it is at LHR Terminal 5 (and even know where in Terminal 5 it is) ... and i'm fairly confident I will eventually get to see it again because I know where it is ... It's just frustrating waiting and constantly emailing them with screenshots from the Apple "Find My" app.