feat(processed-audio-sources): phase 4 - runtime filter integration

Add AudioFilterPipeline for chained filter execution on AudioAnalysis.
Wire filter pipelines into AudioColorStripStream, AudioValueStream,
and WebSocket test endpoint. Add hot-update support via
ProcessorManager.refresh_audio_filter_pipelines(). Thread
AudioProcessingTemplateStore through dependency injection hierarchy.

plans/processed-audio-sources/CONTEXT.md

@@ -9,7 +9,7 @@
 - **Test:** `cd server && py -3.13 -m pytest tests/ --no-cov -q`
 
 ## Current State
-Phase 1 (Audio Filter Framework), Phase 2 (Audio Filters), and Phase 3 (Processed Audio Source Model) implemented.
+Phases 1-4 implemented. Phase 4 (Runtime Integration) wired the audio filter pipeline into the stream runtime.
 
 Phase 1 framework:
 - `AudioFilter` base class, `AudioFilterRegistry`, `AudioFilterOptionDef` in `core/audio/filters/`
@@ -93,7 +93,7 @@ _(none yet)_
 | Phase 1 | impl-agent | — | No | Tasks 7+8 skipped (SQLite migration made them obsolete) |
 | Phase 2 | impl-agent | — | No | All 11 filters implemented, no deviations |
 | Phase 3 | impl-agent | — | No | All 11 tasks done; channel/band logic deferred to Phase 4 |
-| Phase 4 | — | — | — | — |
+| Phase 4 | impl-agent | — | No | All 6 tasks done; dependency injection threaded through |
 | Phase 5 | — | — | — | — |
 | Phase 6 | — | — | — | — |
 | Phase 7 | — | — | — | — |