feat(ui): add model override trigger to backlog plan dialog

Added ModelOverrideTrigger component to the "Plan Backlog Changes" dialog,
allowing users to override the global backlog planning model on a per-request
basis, consistent with other dialogs in the application.

Changes:
- Added model override state management to backlog-plan-dialog
- Integrated ModelOverrideTrigger component in dialog header (input mode only)
- Pass model override (or global default) to backlogPlan.generate API call
- UI shows override indicator when model is overridden from global default

The feature uses the existing backlogPlanningModel phase setting as the default
and allows temporary overrides without changing global settings.

Server already supports optional model parameter in the generate endpoint,
so no backend changes were required.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

apps/ui/src/components/views/board-view/dialogs/backlog-plan-dialog.tsx

@@ -23,7 +23,9 @@ import {
 import { getElectronAPI } from '@/lib/electron';
 import { toast } from 'sonner';
 import { cn } from '@/lib/utils';
-import type { BacklogPlanResult, BacklogChange } from '@automaker/types';
+import type { BacklogPlanResult, BacklogChange, ModelAlias, CursorModelId } from '@automaker/types';
+import { ModelOverrideTrigger } from '@/components/shared/model-override-trigger';
+import { useAppStore } from '@/store/app-store';
 
 interface BacklogPlanDialogProps {
   open: boolean;
@@ -53,6 +55,9 @@ export function BacklogPlanDialog({
   const [prompt, setPrompt] = useState('');
   const [expandedChanges, setExpandedChanges] = useState<Set<number>>(new Set());
   const [selectedChanges, setSelectedChanges] = useState<Set<number>>(new Set());
+  const [modelOverride, setModelOverride] = useState<ModelAlias | CursorModelId | null>(null);
+
+  const { phaseModels } = useAppStore();
 
   // Set mode based on whether we have a pending result
   useEffect(() => {
@@ -83,7 +88,9 @@ export function BacklogPlanDialog({
     // Start generation in background
     setIsGeneratingPlan(true);
 
-    const result = await api.backlogPlan.generate(projectPath, prompt);
+    // Use model override if set, otherwise use global default
+    const effectiveModel = modelOverride || phaseModels.backlogPlanningModel;
+    const result = await api.backlogPlan.generate(projectPath, prompt, effectiveModel);
     if (!result.success) {
       setIsGeneratingPlan(false);
       toast.error(result.error || 'Failed to start plan generation');
@@ -96,7 +103,7 @@ export function BacklogPlanDialog({
     });
     setPrompt('');
     onClose();
-  }, [projectPath, prompt, setIsGeneratingPlan, onClose]);
+  }, [projectPath, prompt, modelOverride, phaseModels, setIsGeneratingPlan, onClose]);
 
   const handleApply = useCallback(async () => {
     if (!pendingPlanResult) return;
@@ -358,13 +365,28 @@ export function BacklogPlanDialog({
     }
   };
 
+  // Get effective model (override or global default)
+  const effectiveModel = modelOverride || phaseModels.backlogPlanningModel;
+
   return (
     <Dialog open={open} onOpenChange={(isOpen) => !isOpen && onClose()}>
       <DialogContent className="max-w-2xl">
         <DialogHeader>
-          <DialogTitle className="flex items-center gap-2">
-            <Wand2 className="w-5 h-5 text-primary" />
-            {mode === 'review' ? 'Review Plan' : 'Plan Backlog Changes'}
+          <DialogTitle className="flex items-center justify-between">
+            <div className="flex items-center gap-2">
+              <Wand2 className="w-5 h-5 text-primary" />
+              {mode === 'review' ? 'Review Plan' : 'Plan Backlog Changes'}
+            </div>
+            {mode === 'input' && (
+              <ModelOverrideTrigger
+                currentModel={effectiveModel}
+                onModelChange={setModelOverride}
+                phase="backlogPlanningModel"
+                size="sm"
+                variant="icon"
+                isOverridden={modelOverride !== null}
+              />
+            )}
           </DialogTitle>
           <DialogDescription>
             {mode === 'review'