Advice for repairing shaped glass cabinet doors
If the curve is formed by the framing (only) and the glass itself is flat, the realm of &quot;reasonably possible without breaking the bank&quot; is active.
Actual curved glass is typically insanely expensive (if you are not a furniture factory buying a large amount of it) for reasons that are not hard to figure out - each radius of curvature would be a different item to stock, it's harder to store and handle than flat sheets, etc. etc.
I have successfully made intricate shaped cuts in glass using a &quot;grit-edge&quot; hacksaw blade (a round one, specifically - can cut any direction) - there are also a variety of powered wet-grinding tools made for stained glass work, for instance, or you might simply pay someone who does stained glass to make the cuts for you. Score and snap with curved cuts is possible but experience makes the odds much better (thus the stained glass practitioner might have much better luck than the average person. Or know when and where to &quot;cheat&quot; with alternate tools they probably already own.)
If you saved the splines, re-use them - if some did not survive, replace them with similar wood.
I'd probably use ordinary window glazing putty to set the glass - that's what it's made for - it can be painted if you want the color to be similar to the other door.