Reddit mentions of LiuXia Wall Lamps & Sconces Wall Spotlights Household Wall Washer Modern Minimalist Bedroom Living Room Bedside lamp led Square Indoor Hotel Engineering Aisle Aluminum, 10W, Warm Light

The follow-up comment was kinda trying to give some hints for searching :)
I've realized that it's surprisingly hard to filter out for these things on Amazon, for some reason. I think it understands the exclusion syntax though, so for example if you keep getting a lot of results of a product that's clearly not what you even mean, you can exclude it form the search by typing -theword and gradually when you've done enough excluding, you start to get more and more relevant and better search results. But somehow either Amazon doesn't have very good filtering and tagging methods for the lamps category, or the English language just doesn't have specific enough terminology to tell apart types of lamp fixtures. I've kinda found it easier to search for lamps in German. Neither of the languages are my native language (and I have never studied German), so I am actually being objective by saying this.

Uplighter. Uplight. Searchlight. Spotlight. Floor spot. Desk spot. (Some types of) task light or reading lamp. Wall washer or just washer. (Some types of) sconce. Accent. (Some types of) artwork/painting/picture lights. Adjustable. Eye protection. Bedside. (Some types of) industrial/architect lamp. Clip, clamp on, gooseneck, if you're into those.

Oh yeah and sometimes reading lamps that are meant especially for industrial uses near bed, for example hotel or hospital lights, can offer very minimalistic and space-saving designs. When you see a wall fixture, you can always ask could it, and would it work if converted into a desk/floor version.
https://www.amazon.com/LiuXia-Spotlights-Household-Minimalist-Engineering/dp/B07JBH6T91/

The idea of "eclipse" fixtures might sometimes work too. Not Ikea price range but not luxury price either: The design classic called 'Eclisse' is minimalistic and contains its own modifiable light "eclipser" to limit angle: http://www.noleggiocose.it/wp-content/uploads/2014/02/Artemide-lampada-Eclisse-Vico-Magistretti-2.jpg
With older designs, many of them are still being manufactured and the new ones are more expensive and somewhat more refined and "shiny" in surface feel, while the prices of older individuals are more affordable. You may want to check Etsy or eBay for what kind of vintage nightstand lamps there happens to be for sale, as pairs. Older lamps, if well kept, sometimes offer more unique and intriguing shapes than what's currently available in stores, if you start to feel like everything current looks very similar. It's an option.

I'd probably be quite keen on some spherical spotlight because then its back looks so simple that you don't even process it that much. I always search for those types with the German term "kugellampe" and maybe add "tisch" for table or "spot" if needed. I'm not sure what you'd call those in English, I haven't seen the keywords being mentioned at all, to differentiate with a normal spotlight shaped spot. Globe, maybe?
Edit: Oh yeah, it's sometimes referred to as an eyeball! But as I thought, it's still nowhere near as effective as a search term as the German equivalent.