Improve README with 17 fixes: broken links, missing examples, etc.

[cinar]

Pull Request

Description

A clear and concise description of the changes you've made.

• Fixes # (link to issue if applicable)
• New Feature
• Documentation Update

Checklist

Please ensure your contribution meets the project standards:

• Code is formatted with go fmt.
• Tests have been added or updated.
• All tests pass (go test -v ./...).
• Architectural mandates (zero-dependency, type safety) are respected.

Additional Context

Add any other relevant context or screenshots here.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.79%. Comparing base (bc33582) to head (e0fbda0).

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #67   +/-   ##
=======================================
  Coverage   87.79%   87.79%           
=======================================
  Files          15       15           
  Lines        1090     1090           
=======================================
  Hits          957      957           
  Misses         92       92           
  Partials       41       41           

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