fix(gates): race web task unconditionally when web dashboard exists

[PolyphonyRequiem]

Summary

_handle_gate_with_web decided between CLI and web gate resolution based on self._web_dashboard.has_connections() at the moment the gate was presented. When no WebSocket client was connected at that instant, it committed to the CLI-only path. Under --web-bg there is no attached stdin, and users typically open the per-run dashboard after seeing the gate-waiting notification, so:

1. Gate is presented, has_connections() is False (no one is looking yet).
2. Fall through to gate_handler.handle_gate → blocks on input() with no tty.
3. User opens the per-run dashboard, clicks Approve.
4. gate_response WebSocket message arrives and is put on _gate_response_queue.
5. Nothing awaits the queue — _wait_for_web_gate was never scheduled.
6. Workflow hangs forever. gate_resolved event is never emitted.

Reproduction

• conductor run <workflow> --web-bg
• Wait for a human_gate agent to fire. Do not open the per-run dashboard yet.
• After the terminal shows the gate-waiting notification, open the per-run dashboard and click any option.
• WebSocket frame is sent and acknowledged; no gate_resolved is ever written, workflow stays blocked.

Fix

Only bail to the CLI-only path when there is no web dashboard at all. Whenever self._web_dashboard exists, start both the CLI and web tasks and race them. wait_for_gate_response is happy to await an empty queue until a client eventually connects and clicks, and if the CLI task resolves first the web task is cancelled cleanly (already handled by asyncio.wait(..., return_when=FIRST_COMPLETED) and the pending-cancel loop below).

Risk

Low. The prior has_connections() short-circuit was an optimization to avoid scheduling a web coroutine when clearly unused; removing it costs one extra asyncio.create_task per gate. No behavioral change for CLI-only runs (_web_dashboard is None).

Tests

Existing gate/race path had no test coverage, which is why this regressed silently. Happy to add a regression test covering 'client connects after gate presented' in a follow-up if desired.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
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Additional details and impacted files

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