fix(web): consume plans on new-thread implementation

[UtkarshUsername]

Fixes #978
Continues #1133 (see https://pr-navigator.pages.dev/t3code-utkarsh).

What Changed

This extends plan consumption to the Implement in a new thread flow #1133.

PR 1133 introduced the shared plan-consumption plumbing and applied it to same-thread Implement. This PR wires the remaining caller: when the user chooses Implement in a new thread, the new thread’s thread.turn.start command now includes sourceProposedPlan.

That allows the existing orchestration and runtime-ingestion path to mark the source proposed plan as implemented when the new thread’s implementation turn actually starts, so the original plan thread no longer has the "Plan Ready" label.

Why

Before this change, the same-thread implementation flow consumed the plan, but the new-thread implementation flow still started an implementation turn without identifying which source plan it came from.

That left the original thread in a stale "Plan Ready" state even though the plan was already being implemented elsewhere.

This PR keeps the behavior consistent across both implementation entrypoints by reusing the same source-plan mechanism introduced in PR 1133.

UI Changes

Combined the before/after videos and posted it on X because the files' sizes were too large to upload here: https://x.com/UtkarshUsername/status/2033161459447087223?s=20

PR Context

This PR continues on top of:

• fix/consume-plan-on-same-thread-implementation

See https://pr-navigator.pages.dev/t3code-utkarsh.

Made this a different PR because it solves a different pre-existing problem. Actually, I had solved this first, but changed the order to make reviewing easier.

Checklist

• This PR is small and focused
• I explained what changed and why
• I included a video for animation/interaction changes

Note

Include sourceProposedPlan metadata in orchestration dispatch for new-thread flow

When starting a new thread from a proposed plan, the orchestration action payload in ChatView.tsx now includes a sourceProposedPlan object carrying the originating threadId and planId. This ensures the plan is consumed/associated correctly when a thread is created from it.

^{Macroscope summarized 2617a99.}

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