Tangentially related: If I wanted to play Half-Life: Alyx, and spend as little money as possible whilst still having a good experience, what do I need? (I already own a beefy desktop computer)
It's not very good resolution by today's standards but it's the cheap entry point. Quest 3 (non-S) has resolution comparable to the Steam Frame but costs $250 more.
If you only want to use it for streaming, you might look a used Quest 2, which has similar optics and screens as the 3S. I'm not sure the state of software support or whether its worse CPU/GPU matter for streaming performance. But I bet they're very cheap secondhand by now.
here's a great video about exactly this, might be outdated as it's 6 years old