feat: implement cursor model migration and enhance auto mode functionality

This commit introduces significant updates to the cursor model handling and auto mode features. The cursor model IDs have been standardized to a canonical format, ensuring backward compatibility while migrating legacy IDs. New endpoints for starting and stopping the auto mode loop have been added, allowing for better control over project-specific auto mode operations.

Key changes:
- Updated cursor model IDs to use the 'cursor-' prefix for consistency.
- Added new API endpoints: `/start` and `/stop` for managing auto mode.
- Enhanced the status endpoint to provide detailed project-specific auto mode information.
- Improved error handling and logging throughout the auto mode service.
- Migrated legacy model IDs to their canonical counterparts in various components.

This update aims to streamline the user experience and ensure a smooth transition for existing users while providing new functionalities.

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

@@ -279,8 +279,8 @@ export function PhaseModelSelector({
   }, [codexModels]);
 
   // Filter Cursor models to only show enabled ones
+  // With canonical IDs, both CURSOR_MODELS and enabledCursorModels use prefixed format
   const availableCursorModels = CURSOR_MODELS.filter((model) => {
-    // Compare model.id directly since both model.id and enabledCursorModels use full IDs with prefix
     return enabledCursorModels.includes(model.id as CursorModelId);
   });
 
@@ -300,6 +300,7 @@ export function PhaseModelSelector({
       };
     }
 
+    // With canonical IDs, direct comparison works
     const cursorModel = availableCursorModels.find((m) => m.id === selectedModel);
     if (cursorModel) return { ...cursorModel, icon: CursorIcon };
 
@@ -352,7 +353,7 @@ export function PhaseModelSelector({
     const seenGroups = new Set<string>();
 
     availableCursorModels.forEach((model) => {
-      const cursorId = stripProviderPrefix(model.id) as CursorModelId;
+      const cursorId = model.id as CursorModelId;
 
       // Check if this model is standalone
       if (STANDALONE_CURSOR_MODELS.includes(cursorId)) {
@@ -908,8 +909,8 @@ export function PhaseModelSelector({
 
   // Render Cursor model item (no thinking level needed)
   const renderCursorModelItem = (model: (typeof CURSOR_MODELS)[0]) => {
-    const modelValue = stripProviderPrefix(model.id);
-    const isSelected = selectedModel === modelValue;
+    // With canonical IDs, store the full prefixed ID
+    const isSelected = selectedModel === model.id;
     const isFavorite = favoriteModels.includes(model.id);
 
     return (
@@ -917,7 +918,7 @@ export function PhaseModelSelector({
         key={model.id}
         value={model.label}
         onSelect={() => {
-          onChange({ model: modelValue as CursorModelId });
+          onChange({ model: model.id as CursorModelId });
           setOpen(false);
         }}
         className="group flex items-center justify-between py-2"
@@ -1458,7 +1459,7 @@ export function PhaseModelSelector({
                   return favorites.map((model) => {
                     // Check if this favorite is part of a grouped model
                     if (model.provider === 'cursor') {
-                      const cursorId = stripProviderPrefix(model.id) as CursorModelId;
+                      const cursorId = model.id as CursorModelId;
                       const group = getModelGroup(cursorId);
                       if (group) {
                         // Skip if we already rendered this group