Enhance deployment output logs

[gerteck]

What is the purpose of this pull request?

• Documentation update
• Bug fix
• Feature addition or enhancement
• Code maintenance
• DevOps
• Improve developer experience
• Others, please explain:

Overview of changes:

Adds some extra docs and logging for case of deploying to other repo.

Anything you'd like to highlight/discuss:

Thought i could resolve the incorrect success logging but turns out it is dependency issue.

New logs if deploying with default token to other repos:

gerteck@mac docs % GITHUB_TOKEN=faketoken123 GITHUB_ACTIONS=true GITHUB_REPOSITORY=custardui/custardui GITHUB_WORKSPACE=/tmp markbind deploy --ci
  __  __                  _      ____    _               _ 
 |  \/  |   __ _   _ __  | | __ | __ )  (_)  _ __     __| |
 | |\/| |  / _` | | '__| | |/ / |  _ \  | | | '_ \   / _` |
 | |  | | | (_| | | |    |   <  | |_) | | | | | | | | (_| |
 |_|  |_|  \__,_| |_|    |_|\_\ |____/  |_| |_| |_|  \__,_|
                                                           
 v6.3.1
info: Website generation started at 6:14:38 PM
info: Building assets...
info: Assets built
info: Generating pages...
info: Pages built
info: Site data built
info: Website generation complete! Total build time: 0.653s
info: Build success!
warn: Warning: You are deploying to a repository different from the one running this workflow ("CustardUI/doesntexist" vs "custardui/custardui").
The built-in GITHUB_TOKEN is scoped only to the triggering repository and cannot push to other repositories.
To fix this, create a Personal Access Token (PAT) with "repo" scope, store it as a repository secret (e.g. GH_TOKEN), and run: markbind deploy --ci GH_TOKEN
info: The website has been deployed at: https://custardui.github.io/doesntexist
gerteck@mac docs % 

Testing instructions:

Proposed commit message: (wrap lines at 72 characters)

Add deployment logs for token access

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Checklist: ☑️

• Updated the documentation for feature additions and enhancements
• Added tests for bug fixes or features
• Linked all related issues
• No unrelated changes

---

Reviewer checklist:

Indicate the SEMVER impact of the PR:

• Major (when you make incompatible API changes)
• Minor (when you add functionality in a backward compatible manner)
• Patch (when you make backward compatible bug fixes)

At the end of the review, please label the PR with the appropriate label: r.Major, r.Minor, r.Patch.

Breaking change release note preparation (if applicable):

• To be included in the release note for any feature that is made obsolete/breaking

Give a brief explanation note about:

• what was the old feature that was made obsolete
• any replacement feature (if any), and
• how the author should modify his website to migrate from the old feature to the replacement feature (if possible).

[codecov]

Codecov Report

❌ Patch coverage is 88.23529% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 71.04%. Comparing base (8f368b3) to head (6d48e7d).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
packages/core/src/Site/SiteDeployManager.ts	88.23%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2862      +/-   ##
==========================================
+ Coverage   70.96%   71.04%   +0.07%     
==========================================
  Files         131      131              
  Lines        7085     7117      +32     
  Branches     1639     1653      +14     
==========================================
+ Hits         5028     5056      +28     
- Misses       2051     2055       +4     
  Partials        6        6              

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[Copilot]

Pull request overview

Improves the deployment developer experience by detecting (and clearly messaging) GitHub Actions authentication pitfalls—especially when attempting cross-repository deployments using the default GITHUB_TOKEN.

Changes:

• Add auth-failure detection/wrapping and an early warning when GitHub Actions GITHUB_TOKEN is used for cross-repo deploys.
• Add unit tests for the new auth/warning helpers and the GitHub Actions cross-repo warning path.
• Update the deployment guide with cross-repository PAT guidance and troubleshooting info.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 2 comments.

File	Description
packages/core/src/Site/SiteDeployManager.ts	Adds cross-repo token warning + auth error detection/wrapping around gh-pages publish failures
packages/core/test/unit/Site/SiteDeployManager.test.ts	Adds unit tests for auth error helpers and cross-repo warning behavior
docs/userGuide/deployingTheSite.md	Documents PAT requirement for cross-repo deployments and adds a troubleshooting tip

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[yihao03]

LGTM! Just need abit clarification on the docs

[gerteck]

Updated docs: