Backport of #26414 to release/v7.6

Triggered by @adityapatwardhan on behalf of @TravisEz13

Original CL Label: CL-BuildPackaging

/cc @PowerShell/powershell-maintainers

Impact

REQUIRED: Choose either Tooling Impact or Customer Impact (or both). At least one checkbox must be selected.

Tooling Impact

• Required tooling change
• Optional tooling change (include reasoning)

This change moves package validation from the release pipeline to the package pipeline, improving sequencing and ensuring validation occurs earlier in the process. This is required to maintain proper build pipeline functionality on the release branch.

Customer Impact

• Customer reported
• Found internally

Regression

REQUIRED: Check exactly one box.

• Yes
• No

This is not a regression.

Testing

Original PR was validated through CI pipeline testing. Change affects build/release automation and has been running successfully on main branch. Backport verified by cherry-pick success and will be validated through CI on the release branch.

Risk

REQUIRED: Check exactly one box.

• High
• Medium
• Low

Medium risk because this changes CI/CD pipeline structure, but the change is well-tested on main branch and is necessary to maintain pipeline consistency across branches. The risk is mitigated by the fact that this only moves validation to an earlier stage, reducing overall complexity.