I am currently working on something that requires video graphics to be displayed on something else. Currently the cheapest projector is around $100-$200. But I only need 30 fps and don't need color since the projection is purely informative. I'm thinking of something like a single-laser projector (like the ones at light shows) could be cheaper, but this is a pretty niche use-case and I don't even know what keywords to use.
You've referenced a speed, which is likely not going to be a problem, depending on the driving computer. A Raspberry Pi may not be powerful enough, although the RPi4 seems promising. You've not referenced resolution, which may be more challenging.
The projection part, especially if you need only one color, is partly complete in the form of LCD panels for resin based 3D printers. They use UV lights under the panel and generate B/W masks to expose the resin.
Change the concept of UV LEDs to visible light LEDs, place the panel in line with a suitable lens (fresnel is good) and you have a projector for relatively low cost.
This is the general configuration of today's projectors, with much higher grade components.