feat: live SSE updates for the SCH3DUL3S tab

Add `SchedulesChanged` to the dashboard event channel so the
operator's schedule list updates in real time without requiring a
tab-activation or form-submit refresh.

Backend:
- `dashboard_events.rs`: new `SchedulesChanged { seq, schedules }`
  variant carrying a full `Vec<WireSchedule>` snapshot (same
  snapshot-over-diff rationale as `RebuildQueueChanged`).
- `coordinator.rs`: `emit_schedules_snapshot()` helper — queries the
  scheduled_prompts list, converts to wire shape, broadcasts the event.
- `dashboard.rs`: call `emit_schedules_snapshot()` at the end of each
  operator API handler that mutates a schedule:
  `post_schedule_new`, `post_schedule_fire_now`,
  `patch_schedule`, `post_schedule_cancel`.
- `scheduled_prompts_worker.rs`: call `emit_schedules_snapshot()`
  after each tick that fires schedules, so `last_fired_at_unix`,
  `next_fire_at_unix`, and reaped one-shots surface live.

Frontend:
- `tabs.js`: add `applySchedulesChanged(ev)` — replaces
  `schedulesState` from the snapshot and calls `renderSchedulesList()`.
  Registered in `MUTATION_HANDLERS` as `schedules_changed`.
  Tab-activation re-fetch kept as safety net for approval-path
  inserts and disconnect windows; comment updated to reflect this.

Docs:
- `docs/web-ui/dashboard.md`: document `schedules_changed` event.
- `CLAUDE.md`: add `SchedulesChanged` to the file-map entry.

frontend/packages/dashboard/src/tabs.js

@@ -223,6 +223,10 @@ window.marked = marked;
     // See docs/web-ui.md::Container row for the badge taxonomy.
     renderContainersFromState();
   }
+  function applySchedulesChanged(ev) {
+    schedulesState = (ev.schedules || []).slice();
+    renderSchedulesList();
+  }
   // Map from agent name → highest-priority in-flight queue entry
   // (`running` beats `queued`). Used by the container row renderer
   // to surface "building..." / "meta-updating..." badges on the
@@ -2471,8 +2475,11 @@ window.marked = marked;
   // ─── scheduled prompts ─────────────────────────────────────────────────
   // Backend exposes `/api/schedules` (snapshot), `/api/schedules`
   // (POST, operator-direct submit), `/api/schedules/{id}/cancel`
-  // (whole or per-target). No SSE channel for schedule mutations yet,
-  // so we refresh on tab activation + after every submit/cancel POST.
+  // (whole or per-target), `/api/schedules/{id}` (PATCH edit),
+  // `/api/schedules/{id}/fire-now` (POST). Mutations now emit a
+  // `schedules_changed` SSE event so the list updates live;
+  // `applySchedulesChanged` handles it. Tab-activation re-fetch kept as
+  // a safety net for approval-path inserts and disconnect windows.
   // Local cache lets `refreshTabCounts` show the active count without
   // re-fetching every second.
   let schedulesState = [];
@@ -3596,6 +3603,7 @@ window.marked = marked;
     meta_inputs_changed:     applyMetaInputsChanged,
     meta_update_running:     applyMetaUpdateRunning,
     rebuild_queue_changed:   applyRebuildQueueChanged,
+    schedules_changed:       applySchedulesChanged,
   };
   (function bindDashboardStream() {
     // Route through the SharedWorker so all open hyperhive tabs share
@@ -3650,8 +3658,9 @@ window.marked = marked;
     renderSelectionBar(Array.from(containersState.values()));
     // Keep overflow button active state in sync after tab change.
     updateTabbarOverflow();
-    // Schedules pane has no SSE channel for mutations, so re-fetch
-    // on activation so the operator never lands on stale data.
+    // Re-fetch schedules on activation as a safety net (SSE covers
+    // live mutations but re-sync ensures consistency after disconnect
+    // windows or approval-path inserts that don't yet emit).
     if (target === 'schedules') refreshSchedules();
     // Permissions tables (capabilities + tool-groups) have no SSE channel;
     // fetch both on each activation so the operator sees fresh data.