Refactor core/ into logical sub-packages and split filter files

Reorganize the flat core/ directory (17 files) into three sub-packages:
- core/devices/ — LED device communication (led_client, wled/adalight clients, providers, DDP)
- core/processing/ — target processing pipeline (processor_manager, target processors, live streams, settings)
- core/capture/ — screen capture & calibration (screen_capture, calibration, pixel_processor, overlay)

Also split the monolithic filters/builtin.py (460 lines, 8 filters) into
individual files: brightness, saturation, gamma, downscaler, pixelate,
auto_crop, flip, color_correction.

Includes the ProcessorManager refactor from target-centric architecture:
ProcessorManager slimmed from ~1600 to ~490 lines with unified
_processors dict replacing duplicate _targets/_kc_targets dicts.

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

server/src/wled_controller/storage/wled_picture_target.py

@@ -4,7 +4,7 @@ from dataclasses import dataclass, field
 from datetime import datetime
 from typing import Optional
 
-from wled_controller.core.processor_manager import ProcessingSettings
+from wled_controller.core.processing.processing_settings import ProcessingSettings
 from wled_controller.storage.picture_target import PictureTarget
 
 
@@ -37,7 +37,7 @@ class WledPictureTarget(PictureTarget):
     @classmethod
     def from_dict(cls, data: dict) -> "WledPictureTarget":
         """Create from dictionary."""
-        from wled_controller.core.processor_manager import DEFAULT_STATE_CHECK_INTERVAL
+        from wled_controller.core.processing.processing_settings import DEFAULT_STATE_CHECK_INTERVAL
 
         settings_data = data.get("settings", {})
         settings = ProcessingSettings(