There are a few options that I have seen, although I couldn’t immediately find exactly what I was looking for.
There are some ideas on that page and a bunch more in the related links below. Although you don’t have to use scissor extensions, you could also box joints with a thin dowel or rod going through to made a hinge. Or buy cheap hinges and replace the pins with a bolt and wing nut so you can tighten it once in place.
You could make it so the base of the stand fits under the foot of your chair/couch so it won’t go anywhere, otherwise it would have to be extremely heavy or bolted in to something that won’t easily move. I was originally going to do something similar to this but ended up putting a side table next to my chair at the same height and use a 12" x 12" granite tile as a mouse pad that sits on both and hangs over the arm of the chair closer to me so I can use it comfortably.
I really need to stop being lazy and just custom build an entire recliner with everything built in.