fix(site): refresh the published version index

[thxCode]

What type of PR is this?

/kind bug
/area integrations

What this PR does / why we need it:

• Fetch the shared documentation version index with cache: "no-store" so newly published versions appear when a page loads.
• Reproduced after RC3 publication: the normal browser fetch returned a cached index containing main and RC2, while a fresh request included RC3. Pages serves this index with Cache-Control: max-age=600.
• Preserve the existing loading, error, version-selection, and article-preservation behavior.

Which issue(s) this PR links to:

Relates #708

Special notes for your reviewer:

• The change is limited to the version-index fetch; no documentation tests are added.
• node --check, make site, and git diff --check pass. The site build reports no broken internal links or documentation-route errors.
• The changed fetch expression was executed in the real browser and returned main, RC3, and RC2 without globally disabling browser caching.
• Full make lint passed. The final diff contains only the version-index fetch change.
• RC3 retains its original source revision and published artifacts. Until a later version includes this fix, a hard refresh refreshes the old cached version index.

Does this PR introduce a user-facing change?

Refresh the documentation version index when loading a page so newly published versions are visible without a hard refresh.

[gpustack-code-review]

✅ OpenCodeReview: Review complete: 0 finding(s) across 1 selected item(s).