fix(clients): a running session shows Working only while a turn is active

[rynfar]

Problem

Web and mobile both derive "Working" from session.status === "running" alone. A provider can report running between turns with nothing in flight (Claude's system/status, fixed server-side in #265), and when that happened the sidebar, the mobile thread list, and the mobile status pill all showed a pulsing "Working" for an idle thread. The same assumption leaked into two adjacent decisions: the "latest turn settled" helpers that gate Plan Ready treated any running session as unsettled, and the mobile composer switched its send button to "Queue follow-up" on running alone, while its sibling clear and remove conditions already required an active turn.

This is the client half of the incident from 2026-09-04: the thread that dropped the user's message sat in exactly this state for seven hours, labelled Working.

Fix

A running session is "working" only when it has an active turn. Applied to every derivation that used status alone:

• web: resolveSidebarThreadStatus, resolveThreadStatusPill, isLatestTurnSettled
• mobile: resolveThreadListV2Status, resolveThreadStatus, both settled helpers, and the composer's queue-follow-up condition

With no active turn the status falls through to the honest signals that already exist: background liveness (Delegating, Monitoring), Plan Ready, Completed, or nothing.

Surfaces walked: web sidebar and flat sidebar pill, mobile thread list and status pill, mobile composer. LegacySidebar and ChatView already required an active turn and are unchanged. Desktop wraps web.

Verification

• Five new tests, each watched failing first, across Sidebar.logic.test.ts, session-logic.test.ts, threadListV2.test.ts, and threadPresentation.test.ts. One pre-existing mobile test asserted Working for a running session that named no turn; it now names one.
• Web unit tests for the two files: 206 passed. Mobile tests for the two files: 49 passed.
• vp run -F @t3tools/web typecheck and vp run -F @t3tools/mobile typecheck: clean. vp fmt --check and vp lint on all touched files: clean.

Companion PRs: #264, #265, #266 fix the server side of the same incident.

Model: Claude Fable 5.1. Harness: Pylon (Claude Code provider).

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