Having received a copy of 41755 Nova's Room as part of the 2024 Q1 Activity Support I could test my idea mentioned above - but it turns out the handle slot of the laptop piece is just a hair too small for the flat end of the antenna lever piece:
Undeterred, I kept searching for possibilities and even managed to find some solutions that offered a somewhat stable but definitely illegal connection, made possible by the flexibility and thinness of the laptop material at the slot:
Of course, integrating these connecting pieces into any kind of meaningful MOC is a nontrivial challenge in itself. Not that the Legoland OSHA would approve of them for office use, anyway. But the flame piece might even serve as a power LED (with the possibility of adding actual lighting from below!) if the rest is hidden well.
Another solution is offered by the thickness of the lower part, which can just be held by a Plate, Modified 1 x 1 with U Clip Thick (Vertical Grip) (presumably other clips would be compatible too), if the protruding upper half of the clip is not a visual problem. (Suggested by Hugo)
Or, for more absurd options, one claw of a chain piece can also fit in the same slot - but only if the other claw has free space in front of the laptop.
Then I recalled that a childhood friend, Johnny T. has exactly such a laptop in his office on the Ice Planet, so I asked him to provide some details about his desk and the attachment solution he devised (the same idea suggested by RSchulz).
Apparently, he simply used a black rubber band (presumably from a decommissioned 8000 Pit Droid) to hold the laptop to a black tile, a black 1x2 brick to hold the band taut, and built a desk with two holes for the rubber band to pass through the surface.
The black color of the desk surface and the back wall underneath helps camouflage the openings and the retro desk lamp actually supports the screen of the laptop to prevent it from tipping backward onto its spine.
I hope some of these ideas can serve as an inspiration. And if anyone has other ideas, I'd gladly give them a try.