I'm not sure of what you use and how you set them up when you work, but instead of an under-desk shelf/drawer, how about a small platform to stand your monitor on and your laptop underneath? I made one with some offcuts from some shelves I made. I'm a messy desk kind of person and I find the ability to shove keyboard etc. under the monitor to free up some desk space, for e.g. when I want to use pen and paper, to be most convenient. I haven't worked for a bit now but the photo below is from a few years ago of my WFH set-up, showing the platform - my work laptop is just visible underneath and my own tower case is under the desk. The desk is a cheap but strong and of a decent size from Office World 22 years ago (£70) . . .and I did tidy it up before taking the photo.
A desktop doesn't need to be super thick or heavy as long as it is on a firm, strong base and doesn't bow under weight (which can be prevented by the base it stands on). My desktop is plastic veneered chipboard and 2cm thick.