poc(api): redesign the API changelog page

[walidcavelius]

Summary

Draft POC for the redesigned /api/changelog page. The per-operation API versioning work was split into #38300.

• Adds filter tabs for all changes, breaking changes, and deprecations.
• Adds product and minimum-version filters with result counts, clear-filter actions, and an empty state.
• Adds a version timeline with lifecycle and breaking-change badges, upgrade guidance, and method/type pills.
• Adds an RSS representation and a Changelog entry to the API sidenav.
• Keeps hand-authored placeholder content in data/api/changelog.yaml for the POC; a production implementation would generate it from the OpenAPI versioning extension.

This is a design POC for reviewer walkthrough, not intended to merge as-is.

Test plan

• Visit /api/changelog/ on the preview build.
• Toggle the change-type tabs and confirm entries, version sections, counts, and breaking-change badges update.
• Select product and version filters and confirm Clear filters appears.
• Filter to an empty result and confirm the empty state renders.
• Confirm the filter bar remains below the sticky API toolbar without overlap on desktop widths.
• Confirm the Changelog entry appears in the API sidenav and the RSS output renders newest-first.

[github-actions]

Preview links (active after the build_preview check completes)

New or renamed files

• https://docs-staging.datadoghq.com/walid/versioning-poc-v2/api/changelog/

[jeff-morgan-dd]

Created DOCS-15156 for a closer look from the docs team - thanks!