chore: remove compatibility files and update gitignore

- Remove CLAUDE.md, GEMINI.md, COPILOT.md (use AGENTS.md instead)
- Add .beads/ and .mypy_cache/ to .gitignore
- Remove .beads/ from git tracking

Author: CybotTM

.beads/ai_cli_preparation.db

@@ -41,6 +41,10 @@ node_modules/
 # AI agent session context (not committed)
 claudedocs/
 .serena/
+.beads/
+
+# Type checking cache
+.mypy_cache/
 
 # Runtime directories
 config/