docs: unify VitePress docs categories

[KooshaPari]

Summary

• apply Wave 1 docs unification pattern
• add CategorySwitcher and category pages
• add docs/scripts/generate-doc-index.sh and generated index json
• harden README structure where needed

Notes

• no behavior/runtime code changes

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📥 Commits

Reviewing files that changed from the base of the PR and between 8268d68 and 3f15ef9.

📒 Files selected for processing (2)

• docs/.vitepress/theme/index.ts
• docs/index.md

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch wave3/lane-c-docs-unification

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[KooshaPari]

Closing as superseded by merged docs PR #694 in this rollout.