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/dependencies.py

@@ -0,0 +1,65 @@
+"""Dependency injection for API routes."""
+
+from wled_controller.core.processor_manager import ProcessorManager
+from wled_controller.storage import DeviceStore
+from wled_controller.storage.template_store import TemplateStore
+from wled_controller.storage.postprocessing_template_store import PostprocessingTemplateStore
+from wled_controller.storage.picture_source_store import PictureSourceStore
+
+# Global instances (initialized in main.py)
+_device_store: DeviceStore | None = None
+_template_store: TemplateStore | None = None
+_pp_template_store: PostprocessingTemplateStore | None = None
+_picture_source_store: PictureSourceStore | None = None
+_processor_manager: ProcessorManager | None = None
+
+
+def get_device_store() -> DeviceStore:
+    """Get device store dependency."""
+    if _device_store is None:
+        raise RuntimeError("Device store not initialized")
+    return _device_store
+
+
+def get_template_store() -> TemplateStore:
+    """Get template store dependency."""
+    if _template_store is None:
+        raise RuntimeError("Template store not initialized")
+    return _template_store
+
+
+def get_pp_template_store() -> PostprocessingTemplateStore:
+    """Get postprocessing template store dependency."""
+    if _pp_template_store is None:
+        raise RuntimeError("Postprocessing template store not initialized")
+    return _pp_template_store
+
+
+def get_picture_source_store() -> PictureSourceStore:
+    """Get picture source store dependency."""
+    if _picture_source_store is None:
+        raise RuntimeError("Picture source store not initialized")
+    return _picture_source_store
+
+
+def get_processor_manager() -> ProcessorManager:
+    """Get processor manager dependency."""
+    if _processor_manager is None:
+        raise RuntimeError("Processor manager not initialized")
+    return _processor_manager
+
+
+def init_dependencies(
+    device_store: DeviceStore,
+    template_store: TemplateStore,
+    processor_manager: ProcessorManager,
+    pp_template_store: PostprocessingTemplateStore | None = None,
+    picture_source_store: PictureSourceStore | None = None,
+):
+    """Initialize global dependencies."""
+    global _device_store, _template_store, _processor_manager, _pp_template_store, _picture_source_store
+    _device_store = device_store
+    _template_store = template_store
+    _processor_manager = processor_manager
+    _pp_template_store = pp_template_store
+    _picture_source_store = picture_source_store