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/feature-defaults/feature-defaults-section.tsx

@@ -23,7 +23,7 @@ import {
   SelectValue,
 } from '@/components/ui/select';
 import type { AIProfile } from '@/store/app-store';
-import type { AgentModel } from '@automaker/types';
+import type { ModelAlias } from '@automaker/types';
 
 type PlanningMode = 'skip' | 'lite' | 'spec' | 'full';
 
@@ -36,7 +36,7 @@ interface FeatureDefaultsSectionProps {
   defaultRequirePlanApproval: boolean;
   defaultAIProfileId: string | null;
   aiProfiles: AIProfile[];
-  validationModel: AgentModel;
+  validationModel: ModelAlias;
   onShowProfilesOnlyChange: (value: boolean) => void;
   onDefaultSkipTestsChange: (value: boolean) => void;
   onEnableDependencyBlockingChange: (value: boolean) => void;
@@ -44,7 +44,7 @@ interface FeatureDefaultsSectionProps {
   onDefaultPlanningModeChange: (value: PlanningMode) => void;
   onDefaultRequirePlanApprovalChange: (value: boolean) => void;
   onDefaultAIProfileIdChange: (value: string | null) => void;
-  onValidationModelChange: (value: AgentModel) => void;
+  onValidationModelChange: (value: ModelAlias) => void;
 }
 
 export function FeatureDefaultsSection({
@@ -243,7 +243,7 @@ export function FeatureDefaultsSection({
               <Label className="text-foreground font-medium">Issue Validation Model</Label>
               <Select
                 value={validationModel}
-                onValueChange={(v: string) => onValidationModelChange(v as AgentModel)}
+                onValueChange={(v: string) => onValidationModelChange(v as ModelAlias)}
               >
                 <SelectTrigger className="w-[140px] h-8" data-testid="validation-model-select">
                   <SelectValue />