Do you have any pictures of the broken part?

I would model the part myself, print it myself and check for fit and function. Once the part design and tolerances confirmed, I would then either use a local or remote shop.

Xometry.eu (no affiliation, never used them) appears to be in Europe and outsources to local shops. They have plastic and metal SLS, CNC, sheet metal, and everything else as possibilities. https://xometry.eu/en/direct-metal-laser-sintering/

Another option is to use the Chinese PCB shops. PCBWay has amazing abilities these days: https://www.pcbway.com/rapid-prototyping/manufacture/?type=3&reffercode=TOP

Its probably the easiest to buy another hinge for glass that doesnt require holes on glass like

Then mount it above the broken hinge.

I think metal printing and/or CNC machining could be way over expensive, but please let us know the price if you go that route. If you really want to solve this with 3D printing consider printing it from plastic and reinforcing it with steel (wire, screws, tube, or reuse existing hinge parts), but it will never look good as if you buy a hinge

So, when you say ‘metallic print’? do you mean something like direct metal laser sintering (powder bed and lasers melting to make a solid part,) or the makerforge FDM printers that then sinter the part?

Either of those two will provide a more-than-adequate solution.

If you mean the metal-filled plastics (like Protopasta metal fills,) the weakness is in the plastic- and are comparable to whatever base plastic they use. Though, the iron fill and copper/brass/bronze fills all are high enough in metal content they can corrode as well as take most of the polish with, so they’ll age. the metal is purely cosmetic, though.

the plastic holds up well enough, and how much of a patina they get depends on some factors, but it’s only the surface that gets the patina- the iron fill, for example won’t rust all they way through. The polish is nice, and you can age them (a weak solution of water and vinegar, for iron, as an example,).

If you can print PLA hinges that hold up well, you can expect roughly the same performance, and the only real change you need to make for metal fills is going to a hardned nozzle. Given the structural concerns, I would suggest looking for metal-filled ASA, or similar rather than PLA fill and testing the prints with regular plastic first- metal fills are relatively expensive, after all.

Hinges are often made of sheet metal.

This can be cut, drilled and bent to fit. A vice, a drill, a file, a hammer and hacksaw would be enough for most hinges.

If the door remains suspended with just one hinge a plastic one may work for a short while. The hinge only suspended half the load.

You can also print the hinge with a high infill percentage to improve strength and resist deformation.