feat(processed-audio-sources): phase 1 - audio filter framework

Add the foundation for audio processing filters, mirroring the existing
picture filter/postprocessing template system:
- AudioFilter base class, AudioFilterRegistry, AudioFilterOptionDef
- AudioProcessingTemplate dataclass + SQLite-backed store
- audio_filter_template meta-filter with recursive resolution
- Full REST API: CRUD templates + filter registry discovery
- Dependency injection wired in dependencies.py and main.py

plans/processed-audio-sources/phase-7-testing-polish.md

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+# Phase 7: Testing & Polish
+
+**Status:** ⬜ Not Started
+**Parent plan:** [PLAN.md](./PLAN.md)
+**Domain:** backend
+
+## Objective
+Verify the full feature works end-to-end, write tests, fix any remaining issues, and clean up dead code.
+
+## Tasks
+
+- [ ] Task 1: Write unit tests for each audio filter
+  - Test each filter transforms AudioAnalysis correctly
+  - Test stateful filters maintain and reset state
+  - Test edge cases: empty spectrum, zero rms, all-zero input
+  - Test filter option validation
+- [ ] Task 2: Write unit tests for AudioFilterPipeline
+  - Test chain of filters produces expected output
+  - Test empty pipeline passes through unchanged
+  - Test reset() resets all stateful filters
+- [ ] Task 3: Write integration tests for AudioProcessingTemplateStore
+  - CRUD operations
+  - Template composition (audio_filter_template) expansion
+  - Cycle detection in template composition
+  - Reference validation
+- [ ] Task 4: Write integration tests for ProcessedAudioSource in AudioSourceStore
+  - CRUD operations
+  - Chain resolution (ProcessedAudioSource → ... → CaptureAudioSource)
+  - Cycle detection in source chains
+  - Reference validation (source + template must exist)
+  - Cascade delete checks
+- [ ] Task 5: Write API tests for audio processing template endpoints
+  - Create, read, update, delete
+  - Validation errors (missing fields, invalid filter_ids)
+  - Reference check on delete
+- [ ] Task 6: Write API tests for updated audio source endpoints
+  - Create/update ProcessedAudioSource and CaptureAudioSource
+  - Reject old types (mono, band_extract)
+  - Validation of source/template references
+- [ ] Task 7: Verify backup/restore includes audio processing templates
+  - Create templates, backup, restore, verify they survive
+- [ ] Task 8: Full build verification
+  - `ruff check src/ tests/ --fix` passes
+  - `npx tsc --noEmit` passes
+  - `npm run build` succeeds
+  - `py -3.13 -m pytest tests/ --no-cov -q` — all tests pass
+- [ ] Task 9: Clean up dead code
+  - Remove any remaining imports of `MonoAudioSource`, `BandExtractAudioSource`
+  - Remove old `band_filter.py` if fully superseded by the band_extract filter (or keep if still used elsewhere)
+  - Remove unused schema classes
+  - Verify no orphaned i18n keys
+- [ ] Task 10: Update system health/info endpoints if they enumerate audio source types
+
+## Files to Modify/Create
+- `tests/test_audio_filters.py` — **create** — filter unit tests
+- `tests/test_audio_filter_pipeline.py` — **create** — pipeline tests
+- `tests/test_audio_processing_template_store.py` — **create** — store tests
+- `tests/test_audio_source_store.py` — **modify** — updated for new types
+- `tests/test_audio_processing_templates_api.py` — **create** — API tests
+- `tests/test_audio_sources_api.py` — **modify** — updated for new types
+- Various files — **modify** — dead code cleanup
+
+## Acceptance Criteria
+- All new tests pass
+- All existing tests pass (no regressions)
+- Full build (Python + TypeScript) succeeds
+- Ruff linting passes
+- No dead code referencing removed types
+- Backup/restore round-trips correctly with audio processing templates
+
+## Notes
+- This is the Big Bang verification phase — the first time build + tests are enforced
+- Expect some breakage from Phases 1-6 that needs fixing here
+- Focus on fixing real issues, not cosmetic cleanup
+- `band_filter.py` may still be used by the band_extract filter — check before removing
+
+## Review Checklist
+- [ ] All tasks completed
+- [ ] Code follows project conventions
+- [ ] No unintended side effects
+- [ ] Build passes
+- [ ] Tests pass (new + existing)
+
+## Handoff to Next Phase
+<!-- N/A — final phase -->