refactor(phase3-session-b1): extract upscale, control, social, health into sub-routers

Extracted 4 endpoint groups into separate sub-router modules:
- health.py: 1 endpoint (GET /health)
- upscale.py: 1 endpoint (POST /upscale)
- control.py: 2 endpoints (POST /control/process, GET /control/operations)
- social.py: 2 endpoints (POST /social/optimize, GET /social/platforms/{platform}/formats)

__init__.py now composes these sub-routers into the legacy router.
All 33 routes preserved. No functional changes.

backend/routers/image_studio/social.py

@@ -0,0 +1,88 @@
+"""Social Optimizer endpoints."""
+
+from typing import Dict, Any
+from fastapi import APIRouter, Depends, HTTPException
+
+from .models import SocialOptimizeRequest, SocialOptimizeResponse, PlatformFormatsResponse
+from .deps import get_studio_manager, _require_user_id
+from services.image_studio import ImageStudioManager, SocialOptimizerRequest
+from services.image_studio.templates import Platform
+from middleware.auth_middleware import get_current_user
+from utils.logger_utils import get_service_logger
+
+logger = get_service_logger("api.image_studio")
+router = APIRouter(tags=["image-studio"])
+
+
+@router.post("/social/optimize", response_model=SocialOptimizeResponse, summary="Optimize image for social platforms")
+async def optimize_for_social(
+    request: SocialOptimizeRequest,
+    current_user: Dict[str, Any] = Depends(get_current_user),
+    studio_manager: ImageStudioManager = Depends(get_studio_manager),
+):
+    """Optimize an image for multiple social media platforms with smart cropping and safe zones."""
+    try:
+        user_id = _require_user_id(current_user, "social optimization")
+        logger.info(f"[Social Optimizer] Request from user {user_id}: platforms={request.platforms}")
+
+        platforms = []
+        for platform_str in request.platforms:
+            try:
+                platforms.append(Platform(platform_str.lower()))
+            except ValueError:
+                logger.warning(f"[Social Optimizer] Invalid platform: {platform_str}")
+                continue
+
+        if not platforms:
+            raise HTTPException(status_code=400, detail="No valid platforms provided")
+
+        format_names = None
+        if request.format_names:
+            format_names = {}
+            for platform_str, format_name in request.format_names.items():
+                try:
+                    platform = Platform(platform_str.lower())
+                    format_names[platform] = format_name
+                except ValueError:
+                    logger.warning(f"[Social Optimizer] Invalid platform in format_names: {platform_str}")
+
+        social_request = SocialOptimizerRequest(
+            image_base64=request.image_base64,
+            platforms=platforms,
+            format_names=format_names,
+            show_safe_zones=request.show_safe_zones,
+            crop_mode=request.crop_mode,
+            focal_point=request.focal_point,
+            output_format=request.output_format,
+            options={},
+        )
+
+        result = await studio_manager.optimize_for_social(social_request, user_id=user_id)
+        return SocialOptimizeResponse(**result)
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"[Social Optimizer] ❌ Error: {str(e)}", exc_info=True)
+        raise HTTPException(status_code=500, detail=f"Social optimization failed: {e}")
+
+
+@router.get("/social/platforms/{platform}/formats", response_model=PlatformFormatsResponse, summary="Get platform formats")
+async def get_platform_formats(
+    platform: str,
+    current_user: Dict[str, Any] = Depends(get_current_user),
+    studio_manager: ImageStudioManager = Depends(get_studio_manager),
+):
+    """Get available formats for a social media platform."""
+    try:
+        try:
+            platform_enum = Platform(platform.lower())
+        except ValueError:
+            raise HTTPException(status_code=400, detail=f"Invalid platform: {platform}")
+
+        formats = studio_manager.get_social_platform_formats(platform_enum)
+        return PlatformFormatsResponse(formats=formats)
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"[Platform Formats] ❌ Error: {str(e)}", exc_info=True)
+        raise HTTPException(status_code=500, detail=f"Failed to load platform formats: {e}")