fix: resolve E2E test failures and add Office direct extraction design

- Fix MySQL connection timeout by creating fresh DB session after OCR
- Fix /analyze endpoint attribute errors (detect vs analyze, metadata)
- Add processing_track field extraction to TaskDetailResponse
- Update E2E tests to use POST for /analyze endpoint
- Increase Office document timeout to 300s
- Add Section 2.4 tasks for Office document direct extraction
- Document Office → PDF → Direct track strategy in design.md

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

backend/app/routers/tasks.py

@@ -127,6 +127,17 @@ def process_task_ocr(
             source_file_path=Path(file_path)
         )
 
+        # Close old session and create fresh one to avoid MySQL timeout
+        # (long OCR processing may cause connection to become stale)
+        db.close()
+        db = SessionLocal()
+
+        # Re-fetch task with fresh connection
+        task = db.query(Task).filter(Task.id == task_db_id).first()
+        if not task:
+            logger.error(f"Task {task_id} not found after OCR processing")
+            return
+
         # Update task with results (direct database update)
         task.result_json_path = str(json_path) if json_path else None
         task.result_markdown_path = str(markdown_path) if markdown_path else None
@@ -304,7 +315,25 @@ async def get_task(
             detail="Task not found"
         )
 
-    return task
+    # Extract processing_track from result JSON metadata if available
+    processing_track = None
+    if task.result_json_path:
+        try:
+            import json
+            from pathlib import Path
+            result_path = Path(task.result_json_path)
+            if result_path.exists():
+                with open(result_path) as f:
+                    result_data = json.load(f)
+                    metadata = result_data.get("metadata", {})
+                    processing_track = metadata.get("processing_track")
+        except Exception:
+            pass  # Silently ignore errors reading the result file
+
+    # Create response with processing_track
+    response = TaskDetailResponse.model_validate(task)
+    response.processing_track = processing_track
+    return response
 
 
 @router.patch("/{task_id}", response_model=TaskResponse)
@@ -841,9 +870,9 @@ async def analyze_document(
                 detail="Task file not found"
             )
 
-        # Analyze document
+        # Analyze document (using detect method)
         detector = DocumentTypeDetector()
-        recommendation = detector.analyze(Path(task_file.stored_path))
+        recommendation = detector.detect(Path(task_file.stored_path))
 
         # Build response
         response = DocumentAnalysisResponse(
@@ -852,10 +881,10 @@ async def analyze_document(
             recommended_track=ProcessingTrackEnum(recommendation.track),
             confidence=recommendation.confidence,
             reason=recommendation.reason,
-            document_info=recommendation.document_info or {},
+            document_info=recommendation.metadata or {},
             is_editable=recommendation.track == "direct",
-            text_coverage=recommendation.document_info.get("text_coverage") if recommendation.document_info else None,
-            page_count=recommendation.document_info.get("page_count") if recommendation.document_info else None
+            text_coverage=recommendation.metadata.get("text_coverage") if recommendation.metadata else None,
+            page_count=recommendation.metadata.get("total_pages") if recommendation.metadata else None
         )
 
         logger.info(f"Document analysis for task {task_id}: {recommendation.track} (confidence: {recommendation.confidence})")