I agree about contacting a reputable stained glass shop. It's likely a special glass, maybe something from DelphiGlass.com (not just plain window glass) and needs to be matched. They'll know what it is.

The repair itself may not be that expensive, they'll un-solder the corner joints to get to get the replacement in. Not a pricey repair.

To OP, I don't suggest trying to remove the window yourself, it needs to be supported just right as it is tipped out or you'll break more of it. The service visits to remove and replace the window may cost more than the actual repair. Overall, it should be some hundreds of dollars. I don't think you'll be happy with a clear glass replacement for the panel, and a new door is overkill.