AI visibility: verify visual-agent compatibility of body{visibility:hidden} pattern

## Goal

Confirm that the `body{visibility:hidden}` + JS-unhide-on-theme-init pattern in `layouts/partials/header.html` doesn't cause visual agents (Claude computer-use, ChatGPT vision, Perplexity visual eval) to capture blank pages.

Parent: #7230 (Phase 0)

## Context

The hidden-until-themed pattern prevents flash-of-unstyled-content. JS-disabled browsers would see a blank page, and the same risk applies to visual agents that take screenshots before JS runs or with JS disabled.

## Acceptance criteria

- Test a representative sample of docs-v2 pages (homepage, product landing, deep article, code-heavy page, FAQ) with:
- Claude computer-use screenshot tool
- ChatGPT vision (web browsing)
- Perplexity visual answer engine
- For each: confirm the visual agent reports/perceives meaningful content, not a blank page
- If any agent captures a blank page, file a follow-up PR — options include:
- JS-free fallback (e.g., \`\` stylesheet override that unhides the body)
- Drop the hidden-by-default pattern in favor of a different FOUC mitigation
- Render the body visible by default but apply theme-derived class names via JS
- Document the test results (which agents, which pages, observed vs expected) in this issue

Start with the body-hiding and JS-unhide pattern in layouts/partials/header.html, then inspect the representative docs-v2 pages listed in the issue. Test those pages with Claude computer-use, ChatGPT vision, and Perplexity visual answer engine; done means recording each agent, page, and observed versus expected result in this issue, and filing a follow-up PR if any captures a blank page.

Written by the indexing model from the issue text.