The only issue with ledged and brace with traditional fittings is the draftproof element. They do tend to curl way from the stops in my experience. If you have the money id go for a framed ledge and brace or any other style you fancy made bespoke for you to suit your sizes. If sound / draft proofing is an issue you can put a seal in the door stop that the door shuts tight against cutting out all draft and noise.

You may be able to get this made to order from a window and door company. You can have cat / dog flaps fitted in glass, it doesn't have to be wood. We have one for our dogs, you order the flap, give it to the door company and they order it with the hole needed for the flap, which you then fit. I can't see why they couldn't put an openable window in it. If you're set on wood, then i'd just get a carpenter to make a window to fit the door and then re-glaze the portion underneath. I once put a stained glass window in a front door, if it's wood it's a lot easier to make all sorts.

You can use slim profile, vacuum double glazing units to install double glazing into your doors. The FINEO vacuum glass has 6.7 mm thickness, so almost the same thickness as single glazing https://chameleon-decorators.co.uk/fineo-glass/ 

Are you after a timber shaker door or a mdf door with a vinyl wrap, if timber [ie oak for staining or ash for painted] than about 99.9% of doors will be a standard size of 715h x 496w, and probably be just a frame so you can glaze it your self with a glass of your choosing, for a size of 645h x 496w to suit a 650*500 cabinet you need a bespoke supplier, i use a company in Leicester that can make that, again it will be unglazed. If you're after a vinyl wrap than you shouldn't have any problem finding a door, but at the size you want it will also probably be unglazed, most independants would be able to supply that as there's nothing complicated. You could look at a local joiner and see if they can make it for you.