fix(web): prevent message sync pill layout flicker

[asfires]

What Changed

• Delay the cached-thread sync indicator for 300 ms so routine foreground
  synchronization does not briefly flash.
• Position the indicator outside the measured composer layout so longer syncs
  cannot change the virtualized timeline inset.
• Reset the reveal delay when switching threads.
• Add focused regression coverage for the delay and layout behavior.

Why

Returning to a T3 Code tab intentionally restarts the active thread subscription
from its latest sequence. While waiting for the server's completion marker, an
existing thread briefly enters the synchronizing state.

The sync pill previously participated in the measured composer layout. Appearing
and disappearing changed composerOverlayHeight, which changed the virtualized
timeline's bottom inset twice in quick succession. On scrollable threads, that
caused a visible message-text flicker.

This keeps the foreground synchronization behavior intact while preventing brief
syncs—and any longer visible sync indicator—from changing timeline geometry.

UI Changes

Before: Returning to the tab briefly displays “Syncing messages...” and
reflows a scrollable message timeline (left Chrome tab in the demo video below).

After: Repeated tab switches no longer flash or reflow the timeline (right Chrome tab in the demo video below).

Screencast.from.2026-08-18.16-12-31.webm

Testing

• vp test run apps/web/src/threadSync.test.ts apps/web/src/components/chat/ThreadSyncStatusPill.test.tsx
• vp run --filter @t3tools/web typecheck
• Targeted lint, formatting, and git diff --check

Checklist

• This PR is small and focused
• I explained what changed and why
• I included before/after evidence for the UI change
• I included a video for the interaction change

Implemented with GPT-5.6-sol through the Codex harness in T3 Code.