util: Drop permission constraints in the release action

[vlasebian]

Summary

The permission constraints added in #1456 prevent the release of the docs. This PR reverts them.

Screenshots

N/A

Changes

• Revert the change in permission constraints in the release jobs

Notes for Reviewers

None.

Checklist

• Scope: The referenced issue is addressed, there are no unrelated changes.
• Run Locally: Verified that the docs build using make server, posted screenshots, verified external links. Test with HUGO_PARAMS_SEARCH_ENABLED=true if style changes will affect the search bar.
• New Features Marked: Documentation for new features is marked using the new-in-version shortcode, according to the guidelines in CONTRIBUTING.
• Style Guidelines: Documentation obeys style guidelines in CONTRIBUTING.
• Commits: Commit messages follow guidelines in CONTRIBUTING, there are no fixup commits left.