chore: Split public and internal interface

[pan-kot]

Description

Same changes as in components repo: cloudscape-design/components#4703

How has this been tested?

• Dry-run to live

Review checklist

The following items are to be evaluated by the author(s) and the reviewer(s).

Correctness

• Changes include appropriate documentation updates.
• Changes are backward-compatible if not indicated, see CONTRIBUTING.md.
• Changes do not include unsupported browser features, see CONTRIBUTING.md.
• Changes were manually tested for accessibility, see accessibility guidelines.

Security

• If the code handles URLs: all URLs are validated through the checkSafeUrl function.

Testing

• Changes are covered with new/existing unit tests?
• Changes are covered with new/existing integration tests?

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.75%. Comparing base (ea8f569) to head (edb2795).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #147   +/-   ##
=======================================
  Coverage   87.75%   87.75%           
=======================================
  Files          25       25           
  Lines         343      343           
  Branches       93       94    +1     
=======================================
  Hits          301      301           
  Misses         42       42           

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