You could just bolt a 1U rackmount server to the underside of a desktop. Or get a desk that's 1.75 inches thick, cut a hole of the appropriate size, and recess the server into it. There are lots of under the desk computer mounts, but I haven't seen a recessed one.
Except without the glass top. Or perhaps glass with a very dark tint so that it looks black, but with sufficiently bright internal lighting you can see through it.
The easier and more likely version would be to make the computer fit in a normal desk drawer. Prefer that to a 1U on account of fan size as another commenter mentioned, but being off to one side instead of the whole desk surface has the benefit of not making the whole desk chunkier.
Biggest issue I find with using a 1u case for a client is fan noise - short of some clever modification to the side panels to fit larger fans transverse, it's near impossible to get acceptably quiet 1u fans.
The Sun "pizza box" computer was like that.[1]
You could just bolt a 1U rackmount server to the underside of a desktop. Or get a desk that's 1.75 inches thick, cut a hole of the appropriate size, and recess the server into it. There are lots of under the desk computer mounts, but I haven't seen a recessed one.
[1] https://blog.pizzabox.computer/pizzaboxes/sparcstation/