I'm very familiar with the stack and the pain of trying to livestream video to a browser. If JPEG screenshots work for your clients, then I would just stick with that.
The problem with wolf, gstreamer, moonlight, $third party, is you need to be familiar with how the underlying stack handles backpressure and error propagation, or else things will just "not work" and you will have no idea why. I've worked on 3 projects in the last 3 years where I started with gstreamer, got up and running - and while things worked in the happy path, the unhappy path was incredibly brittle and painful to debug. All 3 times I opted to just use the lower level libraries myself.
Given all of OPs requirements, I think something like NVIDIA Video Codec SDK to a websocket to MediaSource Extensions.
However, given that even this post seems to be LLM generated, I don't think the author would care to learn about the actual internals. I don't think this is a solution that could be vibe coded.
This is where LLMs shine, where you need to dip your toes into really complex systems but basically just to do one thing with pretty straightforward requirements.