Plan mode: "Implement this plan" can stay in plan mode and stall turn startup

[amanthanvi]

Problem

When a user clicks Implement this plan from the plan follow-up card, the next turn can fail in two related ways:

1. Functional mode-switch failure: the next turn still runs with plan-mode behavior (or appears to stall after the initial goal block) instead of switching to implementation mode.
2. UI/state-sync failure: the collaboration mode UI and thread-scoped codex params can remain on plan, causing future turns to keep inheriting plan mode unexpectedly.

Why this is happening

Current plan-accept flow depends on collaboration modes being loaded and resolvable at click time. In race/fallback scenarios (e.g. mode list not yet loaded, stale selection, or only plan available in-memory), the follow-up message can be sent without a safe non-plan override and without persistently updating thread-scoped mode state.

Reproduction

1. Start a thread in plan mode and wait for a plan tool output.
2. Click Implement this plan quickly after reconnect/thread switch (or when mode list is still refreshing).
3. Observe one or more outcomes:
   • turn starts with plan-like behavior instead of implementation behavior,
   • agent emits initial goal block then appears stuck/stopped,
   • collaboration mode UI still shows/sticks to plan for that thread.

Expected behavior

• Clicking Implement this plan should deterministically start the next turn in a non-plan mode.
• UI selection and persisted thread codex params should switch out of plan in lockstep.
• If no safe non-plan mode is currently resolvable, the follow-up turn should still send an explicit neutral mode override rather than inheriting stale plan state.

Proposed fix (frontend-focused)

• Harden mode resolution for plan-accept:
  • prefer default, then code, then first non-plan mode,
  • never fallback to plan for implement action.
• Always send explicit per-turn collaboration-mode option on plan-accept:
  • resolved non-plan payload when available,
  • explicit collaborationMode: null when not.
• Persist thread-scoped collaboration mode id during plan follow-up actions so UI + behavior stay aligned.

Acceptance criteria

• Implement this plan never sends a plan-mode payload.
• In plan-only/empty-mode race states, accept sends explicit neutral override (collaborationMode: null).
• Thread codex params persist collaboration mode transition on accept (non-plan or null).
• Visual collaboration mode state remains consistent after accept, including thread switch/reselect.
• Regression tests cover default/code/non-plan fallback and plan-only/empty-mode race scenarios.