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/upscale.py

@@ -0,0 +1,40 @@
+"""Upscale Studio endpoint."""
+
+from typing import Dict, Any
+from fastapi import APIRouter, Depends, HTTPException
+
+from .models import UpscaleImageRequest, UpscaleImageResponse
+from .deps import get_studio_manager, _require_user_id
+from services.image_studio import ImageStudioManager
+from services.image_studio.upscale_service import UpscaleStudioRequest
+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("/upscale", response_model=UpscaleImageResponse, summary="Upscale Image")
+async def upscale_image(
+    request: UpscaleImageRequest,
+    current_user: Dict[str, Any] = Depends(get_current_user),
+    studio_manager: ImageStudioManager = Depends(get_studio_manager),
+):
+    """Upscale an image using Stability AI pipelines."""
+    try:
+        user_id = _require_user_id(current_user, "image upscaling")
+        upscale_request = UpscaleStudioRequest(
+            image_base64=request.image_base64,
+            mode=request.mode,
+            target_width=request.target_width,
+            target_height=request.target_height,
+            preset=request.preset,
+            prompt=request.prompt,
+        )
+        result = await studio_manager.upscale_image(upscale_request, user_id=user_id)
+        return UpscaleImageResponse(**result)
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"[Upscale Image] ❌ Error: {e}", exc_info=True)
+        raise HTTPException(status_code=500, detail=f"Image upscaling failed: {e}")