chore(ci): gate docs publish on next only

[rsarika]

COMPLETES #< INSERT LINK TO ISSUE >

This pull request addresses

This follow-up PR aligns next with the workflow change needed for task-refactor: we still need task-refactor to remain in the deploy workflow for SDK/package publishing, but we do not want documentation publishing to run from that branch.

by making the following changes

• Added task-refactor to the deploy workflow branch allowlist in .github/workflows/deploy.yml
• Restricted the publish-documentation job to run only when github.ref_name == 'next'
• Kept the rest of the deploy pipeline unchanged

Change Type

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update
• Tooling change
• Internal code refactor

The following scenarios were tested

• The testing is done with the amplify link
• Verified the workflow diff locally
• Confirmed the deploy trigger now includes both next and task-refactor
• Confirmed publish-documentation is gated to next only
• Ran git diff --check successfully

Note:

• This is a follow-up PR against next so the workflow behavior matches the intended task-refactor fix after merge.

The GAI Coding Policy And Copyright Annotation Best Practices

• GAI was not used (or, no additional notation is required)
• Code was generated entirely by GAI
• GAI was used to create a draft that was subsequently customized or modified
• Coder created a draft manually that was non-substantively modified by GAI (e.g., refactoring was performed by GAI on manually written code)
• Tool used for AI assistance (GitHub Copilot / Other - specify)
  • Github Copilot
  • Other - Please Specify
• This PR is related to
  • Feature
  • Defect fix
  • Tech Debt
  • Automation

Tool used for AI assistance:

• OpenAI Codex

Checklist before merging

• I have not skipped any automated checks
• All existing and new tests passed
• I have updated the testing document
• I have tested the functionality with amplify link

[aws-amplify-us-east-2]

This pull request is automatically being deployed by Amplify Hosting (learn more).

Access this pull request here: https://pr-698.d1b38q61t1z947.amplifyapp.com

[rsarika]

Superseded by #699. We do not want the additional task-refactor workflow change on next; this replacement PR is a no-op comment-only change just to get a merge onto next.