refactor (core, react, examples, docs): rename org to organization

[chakrihacker]

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Description

• Rename org to organization for naming consistency
• Provide details that support your chosen implementation, including: breaking changes, alternatives considered, changes to the API, etc.
• grep all the org and rename to organization
• If the UI is being changed, please provide screenshots.

Testing

• All existing tests should pass
• All examples are tested

Checklist

• I have added documentation for new/changed functionality in this PR or in auth0.com/docs
• All active GitHub checks for tests, formatting, and security are passing
• The correct base branch is being used, if not the default branch

[chakrihacker]

The tests will pass once react package changes are merged

[codecov-commenter]

Codecov Report

❌ Patch coverage is 98.27586% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 83.17%. Comparing base (95a276d) to head (5994faa).

Files with missing lines	Patch %	Lines
...ganization/idp-management/use-sso-provider-edit.ts	91.66%	2 Missing ⚠️
...zation-management/use-organization-details-edit.ts	92.30%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #29      +/-   ##
==========================================
+ Coverage   83.13%   83.17%   +0.04%     
==========================================
  Files         125      125              
  Lines       10262    10291      +29     
  Branches     1077     1077              
==========================================
+ Hits         8531     8560      +29     
  Misses       1731     1731              

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[github-actions]

🚀 Preview deployment

Branch: refs/pull/29/merge
Commit: 27cf4da

📝 Preview URL: https://auth0-universal-components-gub4gzb2d-okta.vercel.app

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Updated at 2025-12-24T10:24:42.862Z

[rax7389]

make sure we publish with this version for both core and react

[chakrihacker]

done

[rax7389]

Just Saw this PR dont have any package.json version change for react

[rax7389]

@chakrihacker please add respective labels and description on the PR

[chakrihacker]

Added labels, and updated package.json