Adds `python -m app --check` which verifies:
- All required environment variables are set
- Matrix homeserver is reachable
- Bot access token is valid
- Bot is a member of the announcements room
- Database path is writable
Uses color-coded pass/fail output with actionable hints on failure.
Configures nio with a 10-second timeout and no retries so checks
complete quickly even against unreachable servers.
https://claude.ai/code/session_01DuzWyMMXvLMB4VxEwJyV4X
