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/package.json

@@ -64,6 +64,7 @@
     "marked": "^17.0.1",
     "marked-gfm-heading-id": "^4.1.3",
     "marked-highlight": "^2.2.3",
+    "matrix-bot-sdk": "^0.8.0",
     "ollama": "^0.6.3",
     "openai": "^6.17.0",
     "reflect-metadata": "^0.2.2",