Exception-terminated chat turns are never billed

Problem

#145 added usage recording to two terminal paths of the /chat/message stream that previously ended a turn without billing — client_disconnected (both checkpoints) and loop_detected. One unbilled terminal path remains: a turn that ends via an exception.

When generate_stream() terminates through the captured_exception path (or the outer except fallback), the turn has typically already consumed real Anthropic tokens — model calls and tool iterations happen before the failure — but no record_usage call is reached, so the turn is free.

Where

backend/chat/orchestrator.py, the two terminal error yields (currently ~lines 718 and 724 on main; #159 touches the same region to sanitize the streamed message, so land that first and locate the yields afterwards).

Notes

• Flagged as non-blocking in the #145 review ("the exception/error termination path is the one terminal path still unbilled — not blocking; flagging so it's tracked").
• Billing on the exception path needs the same exactly-once care that #145's review verified for disconnect/loop: no double-count when an exception follows partially-recorded iterations.
• Related: #159 (sanitizes what the error paths stream; no billing changes).

Start in backend/chat/orchestrator.py at generate_stream() and the two terminal error yields around the captured_exception and outer except paths; review #145's usage-recording changes and land #159 first as noted. Done means exception-terminated turns record consumed usage exactly once, including failures after partially recorded iterations, without double-counting.