agent/streaming: ship synthetic done when a turn ends without one

[alex-fedotyev]

Summary

Chats appear stuck mid-step: the session card drops out of the sidebar's "Running" group into the time-grouped list, but the chat detail keeps showing the "thinking..." spinner because isStreaming was never reset.

The previous c439473 fix (tool schemas aborting agent turns) closed one underlying cause. Three remaining cases also leave _run_inner without emitting a terminal event:

1. Post-stream exception. After receive_response yields ResultMessage the loop exits cleanly, but the ~80 lines after that contain unguarded post-stream work (add_message, mark_active, update_session_metadata, record_turn_usage). If any of those raise, the exception propagates up to engine.run() before broadcast_done ever fires.
2. Hung CLI cancelled externally. claude_agent_sdk's receive_response documents "If no ResultMessage is received, the iterator continues indefinitely." When the CLI wedges and the asyncio task is cancelled, the CancelledError handler sends stopped on the normal path, but the WS message can be lost mid-reconnect.
3. Lost WebSocket message during reconnect. The frontend handler had no symmetry: handleSessionRunning enters streaming on is_running:true but never exits on is_running:false.

I confirmed case 1 against a live session in our DB: last_activity_at stuck at connected_at (04:13:13) but updated_at advanced to 04:30:29, consistent with mark_active running but a later DB write failing before broadcast_done.

What changed

Server. StreamBroadcaster gains an _open_turns set with mark_turn_open / is_turn_open / clear_turn_open. broadcast() auto-clears the flag when a terminal event ships (done/stopped/error). engine.run() calls mark_turn_open before _run_inner; its finally checks is_turn_open and ships a synthetic broadcast_done if still set. Single backstop covers all three cases at the source.

Frontend. handleSessionRunning gets a symmetric exit branch. When the active session reports is_running:false while isStreaming is true, it commits any in-flight streaming blocks to messages, clears streamingBlocks, and resets agentStatus to idle. Belt-and-suspenders for the case where even the synthetic done is missed (e.g. WS reconnect drops the done event but redelivers session_running:false).

Test plan

• tests/test_streaming.py::TestOpenTurnTracking: 5 new tests covering each terminal type clearing the flag, non-terminal types not clearing, explicit clear_turn_open, multi-session isolation, and the broadcast_done helper closing the turn
• tests/test_streaming.py + tests/test_sessions.py + tests/test_engine.py: 76/76 pass
• web/ tsc -b clean
• Smoke: open a chat, run a turn that exercises post-stream cleanup, confirm the spinner clears

[alex-fedotyev]

Bumping for review. This is one of five small reliability fixes (#63, #64, #65, #66, #67) that compound: each closes one cause of chats that wedge mid-turn, lose context after restart, or get routed into the wrong session. Happy to split, rebase, or land any of them in any order; they don't depend on each other.

In daily use the chat surface is the single biggest friction right now, so any of these merging would help. Let me know if you want changes.