refactor(core): unify auth error handling and update docs

• Add shared errNilRequest used by all auth types for nil request errors.
• Simplify and standardize error messages for API key and query auth.
• Update README feature list, examples, and Go version requirement.
• Rename defaultHeaders to headers in New and adjust comments.
• Clarify transport tweaking logic in build and improve comments.
• Minor formatting and comment cleanup throughout client and auth code.