Pinned Todo card stays stale after continuing interrupted work

[Siri-Ray]

Summary

After a run is interrupted with unfinished TodoWrite/update_plan items, the pinned Todo card can remain stuck at a stale progress value such as 3/4 even after the user clicks Continue remaining tasks.

Reproduction

1. Start a run that emits a TodoWrite/update_plan snapshot.
2. Interrupt the run after three of four tasks have completed.
3. Click Continue remaining tasks.
4. Let the continuation start without emitting another TodoWrite/update_plan snapshot.

Actual behavior

The pinned card keeps scanning backward to the interrupted run's last snapshot, so the stale 3/4 state and Continue action remain visible indefinitely.

Expected behavior

Once the continuation is accepted, the old snapshot should leave the pinned slot. A genuinely new TodoWrite/update_plan event should show a fresh card, even if its item content matches the old snapshot.

Root cause

The pinned Todo selector treats the most recent historical Todo event as conversation-global state. The Continue action starts a new turn but does not invalidate the event it is continuing.

[lefarcen]

Hey @Siri-Ray, thanks for writing this up so precisely. I checked the current pinned-Todo path and your diagnosis matches the code: latestTodoWriteInputForPinnedCard() in apps/web/src/runtime/todos.ts walks backward across the whole conversation, and PinnedTodoSlot in apps/web/src/components/ChatPane.tsx renders that result directly, so a continuation turn with no fresh Todo event keeps showing the interrupted run's last 3/4 snapshot.

There is already a fix PR open for this in #6307, which looks like the right place to track the implementation. Once that lands, the pinned slot should clear as soon as the continuation is accepted, and only reappear if the new turn emits a fresh TodoWrite / update_plan snapshot.