feat: add default stage configs when creating competitions from scratch

When creating a competition without a template, the modal now provides
sensible default configurations for each competition type:

- league: round_robin stage with standard points (3/1/0)
- tournament: single_elimination stage
- challenge: rating_delta_challenge stage with sum metric (leaderboard)
- hybrid: group stage + knockout stage

This ensures stages are created automatically instead of leaving
competitions with 'No stages configured yet'.

src/app/[locale]/admin/facilities/[facility_id]/competitions/CreateCompetitionModal.tsx

@@ -59,6 +59,62 @@ const visibilityOptions: { value: CompetitionVisibility; label: string; descript
   { value: 'private', label: 'Private', description: 'Invite only' },
 ];
 
+// Default configs for each competition type when creating from scratch
+const defaultConfigs: Record<CompetitionType, Record<string, unknown>> = {
+  league: {
+    format: {
+      stages: [
+        {
+          type: 'round_robin',
+          name: 'League Stage',
+          rounds: 1,
+          points_win: 3,
+          points_draw: 1,
+          points_loss: 0,
+        },
+      ],
+    },
+  },
+  tournament: {
+    format: {
+      stages: [
+        {
+          type: 'single_elimination',
+          name: 'Main Draw',
+          third_place_match: false,
+        },
+      ],
+    },
+  },
+  challenge: {
+    format: {
+      stages: [
+        {
+          type: 'rating_delta_challenge',
+          name: 'Leaderboard',
+          metric: 'rating_delta_sum', // Total rating gained
+          // Alternative metrics: 'rating_delta_avg', 'rating_delta_max', 'matches_played'
+        },
+      ],
+    },
+  },
+  hybrid: {
+    format: {
+      stages: [
+        {
+          type: 'round_robin',
+          name: 'Group Stage',
+          rounds: 1,
+        },
+        {
+          type: 'single_elimination',
+          name: 'Knockout Stage',
+        },
+      ],
+    },
+  },
+};
+
 export default function CreateCompetitionModal({
   isOpen,
   onClose,
@@ -144,6 +200,9 @@ export default function CreateCompetitionModal({
       return;
     }
 
+    // Use template config if selected, otherwise use default config for the type
+    const config = selectedTemplate?.config ?? defaultConfigs[formData.type];
+
     const request: CreateCompetitionRequest = {
       type: formData.type,
       sport_id: formData.sport_id,
@@ -159,7 +218,7 @@ export default function CreateCompetitionModal({
         ? new Date(formData.registration_close_at).toISOString()
         : undefined,
       template_id: selectedTemplate?.template_id,
-      config: selectedTemplate?.config,
+      config,
     };
 
     try {