[codex] fix docs for current public API

[EdamAme-x]

Fixes #188.

What changed

• Updated authentication examples to match the current async login helpers and init options.
• Reworked the utilities page to remove the obsolete @evex/linejs/utils entrypoint and point to the current public surfaces.
• Corrected method examples and package README references that were stale.

Validation

• deno task docs:build
• markdown link/path checks against local files and GitHub blob targets