feat(FN-3105): add planning depth selection to planning flows

- Add planning depth controls and styling in PlanningModeModal with updated modal reentry behavior
- Thread selected depth through legacy frontend API calls and planning route handlers
- Extend planning prompt builder/runtime wiring to honor depth values for subtask planning
- Add route, planning, and modal tests covering depth selector behavior and validation

Fusion-Task-Id: FN-3105

packages/dashboard/app/components/PlanningModeModal.css

@@ -387,6 +387,58 @@
   text-align: left;
 }
 
+.planning-depth-selector {
+  display: flex;
+  align-items: flex-end;
+  justify-content: center;
+  gap: var(--space-md);
+  max-width: 520px;
+  margin: 0 auto;
+  width: 100%;
+}
+
+.planning-depth-chip-group {
+  display: flex;
+  flex-wrap: wrap;
+  gap: var(--space-sm);
+}
+
+.planning-depth-chip.btn {
+  border-radius: var(--radius-pill);
+  background: var(--surface);
+  border: 1px solid var(--border);
+  color: var(--text);
+  min-height: calc(var(--space-lg) + var(--space-xl));
+  padding: var(--space-sm) var(--space-md);
+}
+
+.planning-depth-chip.btn:hover {
+  border-color: var(--todo);
+  background: var(--card-hover);
+}
+
+.planning-depth-chip-active.btn,
+.planning-depth-chip-active.btn:hover {
+  background: var(--todo);
+  border-color: var(--todo);
+  color: var(--bg);
+}
+
+.planning-depth-question-count {
+  display: flex;
+  flex-direction: column;
+  gap: var(--space-xs);
+  align-items: flex-start;
+  font-size: 12px;
+  color: var(--text-muted);
+}
+
+.planning-depth-question-input.input {
+  width: calc(var(--space-2xl) * 2 + var(--space-xs));
+  min-height: calc(var(--space-lg) + var(--space-xl));
+  padding: var(--space-xs) var(--space-sm);
+}
+
 .session-lock-overlay {
   position: absolute;
   inset: 0;
@@ -1223,6 +1275,20 @@
     border-radius: var(--radius-lg);
   }
 
+  .planning-depth-selector {
+    flex-direction: column;
+    align-items: stretch;
+    gap: var(--space-sm);
+  }
+
+  .planning-depth-chip-group {
+    justify-content: flex-start;
+  }
+
+  .planning-depth-question-count {
+    align-items: flex-start;
+  }
+
   .planning-deps-list {
     flex-direction: column;
     flex-wrap: nowrap;