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Any glass shop worth their salt should be able to form and cut that piece of glass. The artwork painted on the back is going to be the major challenge.
But the chief concern I have is that the cabinet itself has probably become unglued at its edges to the point where there is no longer any dimensional stability, and the cabinet is freely wracking with handling, thus the diagonal crack. Put on a new piece of glass, and you'll be fine--until you need to pick up and move the set elsewhere, and you may be back to square one.
The cabinet is probably chock-a-block full of triangular pieces of wood stock in all the inside corners. You need to make sure that all the joint gluings are still intact on these if you want it to keep the next piece of glass you install.
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