fix(agent-chat): stop labeling a live run as interrupted after a workspace switch

[Zeus-Deus]

Problem

Switching workspaces unmounts the inactive workspace's chat pane while its run keeps going in the backend. On switch-back, the remount hydrate recomputes the interrupted flag purely from the persisted transcript: a healthy mid-flight run has no turn_completed after its last user turn yet, so lastTurnUnsettled flags it and the pane shows a false "Run interrupted" divider + Continue run chip over a run that is actually alive (it then "continues by itself" once the next live event clears the flag).

Subagent-heavy runs hit this reliably: their item_completed rows grow the disk transcript past the frozen in-memory slice, which is exactly the condition that lets the remount hydrate guard pass.

Fix

Give hydrate an authoritative liveness signal instead of the heuristic alone:

• AgentProvider::turn_active — new default trait method: true iff a live (non-dead) session is bound to the thread and its active_turn is set. Cheap in-memory check, never touches the subprocess. Implemented for Claude and Codex via the sessions map, and for OpenCode via the SSE event-context flag behind the same absent/dead guards.
• agent_chat_turn_active — new read-only command exposing it (no auto-resume).
• The remount hydrate effect probes it after fetching payloads (if the turn settles between the two calls, the settling turn_completed row is already in the payloads — a stale "alive" answer can't mislabel a finished run) and threads { runLive } through hydrateThread → replayPayloads. runLive: true forces interrupted: false and sets streaming: true so the streaming marker shows instead of the divider. A probe error degrades to false (previous behavior).
• Dev mock implements the command from its in-flight turn set; docs/features/agent-chat.md documents the new guard and command.

The genuine cases keep working: dead-run detection (child-exit watchdog, app-died-mid-turn hydrate) still surfaces the divider and Continue chip.

Verification

• npm run verify green: cargo check + cargo test, tsc, vitest (171 files / 2522 tests).
• New tests: Rust adapter coverage for unknown-thread / in-flight / settled / dead-session on Claude and Codex; hydrate unit tests for the runLive override (incl. overriding a replay-observed child_exited); pane tests for probe-true, probe-rejected fallback, and arg routing.
• Exercised end to end in the browser against the dev mock: the probe flips false → true → false across a streamed turn; switching away and back mid-run no longer surfaces the divider; a genuine child_exited interrupt still renders the divider + Continue chip.