Refactor capture engine architecture, rename PictureStream to PictureSource, and split API modules

- Separate CaptureEngine into stateless factory + stateful CaptureStream session
- Add LiveStream/LiveStreamManager for shared capture with reference counting
- Rename PictureStream to PictureSource across storage, API, and UI
- Remove legacy migration logic and unused compatibility code
- Split monolithic routes.py (1935 lines) into 5 focused route modules
- Split schemas.py (480 lines) into 7 schema modules with re-exports
- Extract dependency injection into dedicated dependencies.py

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

server/src/wled_controller/api/schemas/common.py

@@ -0,0 +1,52 @@
+"""Shared schemas used across multiple route modules."""
+
+from datetime import datetime
+from typing import Dict, List, Optional
+
+from pydantic import BaseModel, Field
+
+
+class ErrorResponse(BaseModel):
+    """Error response."""
+
+    error: str = Field(description="Error type")
+    message: str = Field(description="Error message")
+    detail: Optional[Dict] = Field(None, description="Additional error details")
+    timestamp: datetime = Field(default_factory=datetime.utcnow, description="Error timestamp")
+
+
+class CaptureImage(BaseModel):
+    """Captured image with metadata."""
+
+    image: str = Field(description="Base64-encoded thumbnail image data")
+    full_image: Optional[str] = Field(None, description="Base64-encoded full-resolution image data")
+    width: int = Field(description="Original image width in pixels")
+    height: int = Field(description="Original image height in pixels")
+    thumbnail_width: Optional[int] = Field(None, description="Thumbnail width (if resized)")
+    thumbnail_height: Optional[int] = Field(None, description="Thumbnail height (if resized)")
+
+
+class BorderExtraction(BaseModel):
+    """Extracted border images."""
+
+    top: str = Field(description="Base64-encoded top border image")
+    right: str = Field(description="Base64-encoded right border image")
+    bottom: str = Field(description="Base64-encoded bottom border image")
+    left: str = Field(description="Base64-encoded left border image")
+
+
+class PerformanceMetrics(BaseModel):
+    """Performance metrics for template test."""
+
+    capture_duration_s: float = Field(description="Total capture duration in seconds")
+    frame_count: int = Field(description="Number of frames captured")
+    actual_fps: float = Field(description="Actual FPS (frame_count / duration)")
+    avg_capture_time_ms: float = Field(description="Average time per frame capture in milliseconds")
+
+
+class TemplateTestResponse(BaseModel):
+    """Response from template test."""
+
+    full_capture: CaptureImage = Field(description="Full screen capture with thumbnail")
+    border_extraction: Optional[BorderExtraction] = Field(None, description="Extracted border images (deprecated)")
+    performance: PerformanceMetrics = Field(description="Performance metrics")