feat(#378): Install matrix-bot-sdk and create MatrixService skeleton

- Add matrix-bot-sdk dependency to @mosaic/api
- Create MatrixService implementing IChatProvider interface
- Support connect/disconnect, message sending, thread management
- Parse @mosaic and !mosaic command prefixes
- Delegate commands to StitcherService (same flow as Discord)
- Add comprehensive unit tests with mocked MatrixClient (31 tests)
- Add Matrix env vars to .env.example

Refs #378

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

apps/api/src/bridge/matrix/index.ts

@@ -0,0 +1 @@
+export { MatrixService } from "./matrix.service";