Using DocSearch v4 beta with Docusaurus & VitePress

[dylantientcheu]

🔗 Please read & comment here instead: #2681

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Hi everyone 👋,

We’re tracking all feedback for the DocSearch v4 beta integration with Docusaurus & VitePress in the Discussion thread linked above.

• Do not open new issues about the tarball workaround, peer-deps, or Ask AI config. Rather, post in the Discussion so we keep everything in one place.
• The current tarball/resolutions approach is temporary.
  We’re collaborating with both Docusaurus and VitePress maintainers to ship proper v4 support in their next release cycles.
• Once upstream packages are out, we’ll deprecate this patch and update the docs accordingly.

Thanks for helping us keep the tracker tidy!