Is it possible to wire up a simple camera module with a separate wifi module to create a live UDP stream without full fledged OS?
There are products based on well known modules like the ESP32 that provide camera and network interfaces. One such example I've found is the "AI-Thinker ESP32-CAM".



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When you go for a known module you get the benefit of having plenty of resources available to help you get it up and running. For example, you could follow a tutorial and more easily end up with a working system you could use as a starting point for your final project.