Many of those types of cabinets separate easily--mine has cast iron braces to hold the top on the base, so separating them to use in the same space is no big deal, IMO, and removing a door is a good solution, if you want to use the two pieces in the same room. I'd save the door, and all hardware, and keep it nearby, in case you want to restore the cabinets. The 'top only' piece makes that a moot point, so I'd choose it, and the other cabinet which most closely matches, and would be most suitable for a desk. I like option #2. You can replace the glass panels to match one or the other, and keep the originals with the door and hardware. My cabinet has replacement glass panels, done by my sister before she gave me the cabinet. ETA, as for height, you can get a wooden island stool, and cut the legs down to the correct height for the countertop. We did that once with two matching stools, when toddlers needed an interim chair height between high chair and regular chair.

Can you clarify what you mean by you would not do a painted desk top? The closet companies uniformly recommended doing a Formica desk too for durability rather than melamine like the rest of the built in but said that I could do white melamine to have it all in white. The cabinetmakers said it would all be painted wood in a color of my choice.

Very helpful that you gave your pallet and thoughts. Choose your countertop and then your desk and cabinet colors. Countertop colors are limited, while paint colors are infinite. You can color match to Silestone Altair since you like that one - then go a shade darker or lighter for a nice color flow. Your pallet is very dark - except for the golden/beige walls- ranging from a black/brown to a brown/green. These are tones we used more in the 2000's so be sure and choose updated lines in the furnishings or the room will look dated already. The floor is beautiful! For the rest of the furnishings - choose a light colored rug, chairs in a beige or bring in a pop of a rich blue. Definitely add some greenery in natural stone pots on your shelving to bring in nature. A large, modern art piece would keep the vive fresh in this traditional space.

Please post pictures of the room.