[DOCS-XXXXX] Add Authorize Private Actions

[irving-santiago]

What does this PR do? What is the motivation?

Fixes DOCS-XXXXX

Adds a new "Authorize Private Actions" page comparing the two authorization models (Connections vs. Execution Policies) and explaining which one applies to a given runner based on its ownership.

Merge readiness

• Ready for merge

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AI assistance

Claude Code carried this page's content over from a pre-drafted, QA-verified draft, ran Vale, and fixed an invalid front-matter YAML value and a couple of style-guide word-choice issues. After a post-implementation structure review against the original plan, also fixed 3 places where the draft listed Connections before Execution Policies (a section order, a comparison table's columns, and a bullet list), which violated this project's standing ordering convention (Execution Policies/ownerless before Connections/owned).

Additional notes

[irving-santiago]

Warning

This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
Learn more

• [DOCS-XXXXX] Add Get Started with Private Actions (Execution Policies quickstart) #39054
• [DOCS-XXXXX] Add Private Actions Reference #39053
• [DOCS-XXXXX] Rewrite Run a Script for Execution Policies #39052
• [DOCS-XXXXX] Add Execution Policies #39051
• [DOCS-XXXXX] Add Authorize Private Actions #39050 👈 (View in Graphite)
• [DOCS-XXXXX] Add Enrollment and Ownership #39049
• [DOCS-XXXXX] Add Set Up a Standalone Private Action Runner #39048
• [DOCS-XXXXX] Rewrite Set Up in the Datadog Agent, add Execution Policies enrollment #39047
• [DOCS-XXXXX] Move Handling Private Action Credentials under Connections #39046
• [DOCS-XXXXX] Rewrite Private Actions Overview for Execution Policies #39045
• Add tracking doc for the Private Actions / Execution Policies stack #39044
• master

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[github-actions]

Preview links (active after the build_preview check completes)

New or renamed files

• https://docs-staging.datadoghq.com/irving.santiago/par-ep-06-authorize/actions/private_actions/authorize_private_actions