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/__init__.py

@@ -1,5 +1,18 @@
 """API routes and schemas."""
 
-from .routes import router
+from fastapi import APIRouter
+
+from .routes.system import router as system_router
+from .routes.devices import router as devices_router
+from .routes.templates import router as templates_router
+from .routes.postprocessing import router as postprocessing_router
+from .routes.picture_sources import router as picture_sources_router
+
+router = APIRouter()
+router.include_router(system_router)
+router.include_router(devices_router)
+router.include_router(templates_router)
+router.include_router(postprocessing_router)
+router.include_router(picture_sources_router)
 
 __all__ = ["router"]