fix: Multiple compilation fixes per PROMPT.md
Video module:
- Fix state.db -> state.conn field name
- Fix analytics.rs imports placement
- Remove AppState dependency from websocket.rs (use global broadcaster)
- Simplify render.rs broadcaster usage
Other modules:
- Add sha1 crate dependency
- Fix AppState import paths (project, legal)
- Fix db_pool -> conn throughout codebase
- Add missing types: RefundResult, ExternalSyncError, TasksIntegrationError, RecordingError, FallbackAttemptTracker
- Add stub implementations for GoogleContactsClient, MicrosoftPeopleClient
- Fix social/mod.rs format string
- Fix designer/canvas.rs SVG path
- Remove doc comments per PROMPT.md
- Add missing handler implementations in calendar_integration.rs