feat(ui): Enhance AI model handling with Cursor support

- Refactor model handling to support both Claude and Cursor models across various components.
- Introduce `stripProviderPrefix` utility for consistent model ID processing.
- Update `CursorProvider` to utilize `isCursorModel` for model validation.
- Implement model override functionality in GitHub issue validation and enhancement routes.
- Add `useCursorStatusInit` hook to initialize Cursor CLI status on app startup.
- Update UI components to reflect changes in model selection and validation processes.

This update improves the flexibility of AI model usage and enhances user experience by allowing quick model overrides.

apps/ui/src/components/views/settings-view/phase-models/phase-model-selector.tsx

@@ -1,13 +1,14 @@
 import { cn } from '@/lib/utils';
 import { useAppStore } from '@/store/app-store';
-import type { AgentModel, CursorModelId } from '@automaker/types';
+import type { ModelAlias, CursorModelId } from '@automaker/types';
+import { stripProviderPrefix } from '@automaker/types';
 import { CLAUDE_MODELS, CURSOR_MODELS } from '@/components/views/board-view/shared/model-constants';
 
 interface PhaseModelSelectorProps {
   label: string;
   description: string;
-  value: AgentModel | CursorModelId;
-  onChange: (model: AgentModel | CursorModelId) => void;
+  value: ModelAlias | CursorModelId;
+  onChange: (model: ModelAlias | CursorModelId) => void;
 }
 
 export function PhaseModelSelector({
@@ -20,13 +21,10 @@ export function PhaseModelSelector({
 
   // Filter Cursor models to only show enabled ones
   const availableCursorModels = CURSOR_MODELS.filter((model) => {
-    const cursorId = model.id.replace('cursor-', '') as CursorModelId;
+    const cursorId = stripProviderPrefix(model.id) as CursorModelId;
     return enabledCursorModels.includes(cursorId);
   });
 
-  // Check if current value is a Claude model or Cursor model
-  const isClaudeModel = (v: string) => ['haiku', 'sonnet', 'opus'].includes(v);
-
   return (
     <div
       className={cn(
@@ -50,7 +48,7 @@ export function PhaseModelSelector({
             return (
               <button
                 key={model.id}
-                onClick={() => onChange(model.id as AgentModel)}
+                onClick={() => onChange(model.id as ModelAlias)}
                 className={cn(
                   'px-3 py-1.5 rounded-lg text-xs font-medium',
                   'transition-all duration-150',
@@ -75,7 +73,7 @@ export function PhaseModelSelector({
 
           {/* Cursor Models */}
           {availableCursorModels.map((model) => {
-            const cursorId = model.id.replace('cursor-', '') as CursorModelId;
+            const cursorId = stripProviderPrefix(model.id) as CursorModelId;
             const isActive = value === cursorId;
             return (
               <button