feat(05-03): Implement API fallback handling for research display

- Enhanced exaSearch service with Exa API + fallback tier system
  * Tier 1: Exa API (primary)
  * Tier 2: Synthetic results with suggested web sources
  * Improved error handling with graceful degradation

- Updated backend exerciseResearch route to return provider info
  * Returns 'provider' field identifying which API was used
  * Returns 'status' field (success/degraded) for UI feedback
  * Better error messages for debugging

- Enhanced ResearchDisplay component with fallback feedback
  * New ResearchProviderBadge shows which provider was used
  * Visual indicators for fallback results (Suggested badge)
  * Support for multiple provider types (exa, fallback, gemini, etc.)
  * Improved error handling and recovery flows

- Updated ExerciseResearchPanel with better error handling
  * Proper response parsing from backend
  * Forwards provider and status info to display component
  * Improved accessibility with tooltip hints

- Added comprehensive Research Display styling
  * Responsive layout for mobile and desktop
  * Visual hierarchy for summaries and sources
  * Provider badge styling with color-coding
  * Fallback state indicators for user awareness

backend/src/routes/exerciseResearch.js

@@ -45,7 +45,8 @@ const createExerciseResearchRouter = ({ pool, exaSearch }) => {
         ? Math.min(requestedResults, 10)
         : 5;
 
-      const { summary, results } = await exaSearch({ query, numResults });
+      // Fetch research with fallback support
+      const { summary, results, provider, status } = await exaSearch({ query, numResults });
 
       let researchRecord = null;
       try {
@@ -53,7 +54,7 @@ const createExerciseResearchRouter = ({ pool, exaSearch }) => {
           `INSERT INTO research_results (exercise_id, query, summary, results, provider)
            VALUES ($1, $2, $3, $4, $5)
            RETURNING id, created_at`,
-          [exerciseId, query, summary, JSON.stringify(results), 'exa']
+          [exerciseId, query, summary, JSON.stringify(results), provider || 'exa']
         );
         researchRecord = insertResult.rows[0] || null;
       } catch (err) {
@@ -65,11 +66,16 @@ const createExerciseResearchRouter = ({ pool, exaSearch }) => {
         query,
         summary,
         results,
-        stored: researchRecord
+        stored: researchRecord,
+        provider: provider || 'exa',
+        status: status || 'success'
       });
     } catch (err) {
       console.error('Error running exercise research:', err);
-      res.status(500).json({ error: 'Failed to fetch research' });
+      res.status(500).json({ 
+        error: 'Failed to fetch research',
+        message: err.message 
+      });
     }
   });