chore: add Biome as linter + formatter (#32)

- Install @biomejs/biome with project-wide configuration
- Auto-fix formatting and lint issues across all packages
- Fix pre-existing typecheck issue (Executor.callTool visibility)
- Configure sensible rule overrides for the codebase
- Remove turbo lint task (Biome runs at root level)

Closes #22

Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>

Author: ceilf6