That is not actually a "data race". It is a race condition for sure, but a data race is a very specific thing - where two threads access the same location at the same time and at least one is a write.
That could be unsafe in Rust because it might lead to reading "impossible values" like an enum that isn't equal to any of its variants. Therefore safe Rust must prevent it or there's a soundness hole.
Yeah... I mean they should have just copied whatever video conferencing platforms do because they all work fine behind corporate proxies and they also don't suffer from this "increasing delay" problem.
I haven't actually looked into what they do but presumably it's something like webrtc with a fallback to HLS with closed loop feedback about the delay.
Though in fairness it doesn't sound like "watching an AI agent" is the most critical thing and mjpeg is surprisingly decent.