Is your feature request related to a problem? Please describe.
For streaming functions (e.g. /run_sse), once the stream is started (http response code 200), there's no way currently to know if an error happened mid stream. This makes it hard to appropriately message to the user what might have happened.

Describe the solution you'd like
SSE error events would be perfect way to handle this. Exactly what this comment mentions.

Describe alternatives you've considered
No alternatives as far as I'm aware.