CI: Build docs in-place

[pblazej]

It turned out to be a little flaky (artifacts out-of-sync), build cost is still negligible here.

Example: https://github.com/livekit/client-sdk-swift/actions/runs/21626345080

Optionally, we can remove them from CI workflow (it may lead to unpleasant surprises tho).

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📥 Commits

Reviewing files that changed from the base of the PR and between 8546516 and da8abf8.

📒 Files selected for processing (1)

• .github/workflows/publish-docs.yaml

✨ Finishing touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch blaze/ci-fix-docs

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[github-actions]

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