[CI/a11y] Add automated heading-hierarchy / axe-core check to site_lint.yml

Currently, accessibility regressions related to heading structure (such as skipping heading levels or incorrect hierarchy order) are not caught automatically by CI during PR checks.

Recently, a heading level skip issue was identified and resolved manually ([link to your PR here]). Integrating an automated accessibility auditor into our CI pipeline would prevent similar regressions from slipping through in the future.

Proposed Solution

• Add an automated accessibility testing tool (such as axe-core, @axe-core/playwright, or an equivalent linting rule/script) to the site_lint.yml GitHub Actions workflow.
• Ensure the check specifically validates heading-order hierarchy rules (e.g., preventing skips like H1 → H3).

Additional Context

• Discussed as a side note in PR https://github.com/reactjs/react.dev/pull/8607#pullrequestreview-4955873812.

• Tooling suggestion: axe-core / eslint-plugin-jsx-a11y or a post-build HTML scan step in CI.

Start by reading the site_lint.yml GitHub Actions workflow and the heading-order discussion in PR 8607. Determine how an axe-core, @axe-core/playwright, eslint-plugin-jsx-a11y, or post-build HTML check fits the existing workflow, then verify that CI catches skipped heading levels such as H1 → H3.