Gate automatic idle turns in Plan mode (#26147)

## Why

Goal idle continuation is extension-triggered model-visible work, so it
should follow one core-owned rule for when automatic work may start. In
particular, it should not jump ahead of queued user/client work, start
while another task is active, or inject a continuation turn while the
thread is in Plan mode.

Keeping this policy in `try_start_turn_if_idle` avoids passing
`collaboration_mode` or review-specific state through
`ThreadLifecycleContributor::on_thread_idle`. Active `/review` is
covered by the same active-task gate because Review turns are not
steerable.

## What Changed

- Teach `Session::try_start_turn_if_idle` to reject automatic idle turns
in Plan mode, both before reserving an idle turn and after building the
turn context.
- Document `CodexThread::try_start_turn_if_idle` as the extension-facing
gate for automatic idle work, including Plan-mode and active Review-task
behavior.
- Add focused coverage for Plan-mode rejection and active Review-task
rejection without queuing synthetic input.

## Testing

- `just test -p codex-core try_start_turn_if_idle`

codex-rs/core/src/lib.rs

@@ -22,6 +22,8 @@ mod config_lock;
 pub use codex_thread::CodexThread;
 pub use codex_thread::CodexThreadSettingsOverrides;
 pub use codex_thread::ThreadConfigSnapshot;
+pub use codex_thread::TryStartTurnIfIdleError;
+pub use codex_thread::TryStartTurnIfIdleRejectionReason;
 pub use session::turn_context::TurnContext;
 mod agent;
 mod attestation;