Track mobile pinned plan panel parity

## Context

PR #1217 moves desktop plan rendering out of the chat stream and into a pinned composer panel. Mobile still keeps the existing in-stream todo card behavior and was intentionally deferred from that PR.

## Follow-up

Bring the mobile control experience to parity with the desktop pinned plan behavior, or document the mobile-specific product decision if the interaction should remain different.

## Acceptance criteria

- Mobile has an explicit plan visibility treatment for current TodoWrite / update_plan / Task* state.
- Device-link mobile control behavior is verified for active desktop sessions.
- Tests or manual verification notes cover the mobile behavior.

Tracking issue created from the remote/mobile adaptation gate on #1217.

Start by reading PR #1217 and tracing the mobile handling of TodoWrite, update_plan, and Task* state alongside the desktop pinned plan behavior. Verify how device-link control behaves for an active desktop session. Done means mobile has an explicit plan-visibility treatment and tests or manual verification notes covering the behavior, or the mobile-specific product decision is documented.

Written by the indexing model from the issue text.