Sorry to hear of your problems.
Whilst loan cars still exist at some service centres they are under high demand and not available for long periods.
My Model S motor failed last year and I had it towed to Tesla on a Sunday. When I went in early on Monday morning they still hadn’t washed the sole loaner vehicle from its return on Friday and I used it for the 3 days it took to repair.
Unfortunately Model X parts would come from USA and with worldwide logistics the way they are the delay is understandable but not really an excuse for such a long delay.
I would talk to the service centre and ask for a loaner rental at least fir a week or so until you can arrange something longer term.