Rewrite Claude provider comparison: AISBF vs vendors/kilocode vs vendors/claude

Document now correctly compares only the three Claude provider implementations:

- AISBF (aisbf/providers.py) - Direct HTTP with OAuth2
- vendors/kilocode (vendors/kilocode/packages/opencode/src/provider/) - AI SDK
- vendors/claude (vendors/claude/src/) - Original Claude Code

All tables and references now use these three sources exclusively.
Removed all Kiro Gateway content which was unrelated to Claude.