Previously, if an error occurred during response processing in
_process_message_background (e.g. during extract_media, send, or
any uncaught exception from the handler), the error was only logged
to server console and the user was left with radio silence — typing
indicator stops but no message arrives.
Now the outer except block attempts to send the error type and detail
(truncated to 300 chars) to the user's chat, matching the format
already used by the inner handler in gateway/run.py.
Co-authored-by: Test <test@test.com>
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