chore: migrate linting and formatting to biome

[Ma11hewThomas]

Summary

• replace ESLint + Prettier with Biome
• add biome configuration modeled on github-test-reporter
• remove legacy eslint/prettier config files
• update package scripts to use biome for lint/format/check
• refresh dependencies and lockfile
• apply biome formatting changes
• fix validate typing to satisfy biome error-level rule

Validation

• npm run format:check
• npm run check
• npm run lint
• npm run all

Notes

• Biome warnings remain in tests (non-blocking), no error-level diagnostics remain.