refactor: improve input mode system and add referral mode

- Refactor isBashMode to flexible InputMode type system
- Fix bash mode entry logic (exact match vs startsWith)
- Add comprehensive referral mode with validation (3-50 alphanumeric chars)
- Improve error handling with try/catch in command handlers
- Add error state to ReferralBanner component
- Make placeholder casing consistent (all lowercase)
- Remove unused isSpecialMode function
- Add 44 referral mode tests covering validation, UI, and error handling
- Update formatElapsedTime to omit redundant 0s (1m vs 1m 0s)

Author: brandonkachen