Attach cookies to client after first request (to support multiple-replica setups with cookie-based affinity)

[abidlabs]

Closes: #10164 (not sure if we have a way to test this yet, @aliabid94?)

[gradio-pr-bot]

🪼 branch checks and previews

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Install Gradio from this PR

pip install https://gradio-pypi-previews.s3.amazonaws.com/8f4b238d2d37bb1aab95669d269ad02bcc3f16e8/gradio-5.25.2-py3-none-any.whl

Install Gradio Python Client from this PR

pip install "gradio-client @ git+https://github.com/gradio-app/gradio@8f4b238d2d37bb1aab95669d269ad02bcc3f16e8#subdirectory=client/python"

Install Gradio JS Client from this PR

npm install https://gradio-npm-previews.s3.amazonaws.com/8f4b238d2d37bb1aab95669d269ad02bcc3f16e8/gradio-client-1.14.2.tgz

Use Lite from this PR

<script type="module" src="https://gradio-lite-previews.s3.amazonaws.com/8f4b238d2d37bb1aab95669d269ad02bcc3f16e8/dist/lite.js""></script>

[gradio-pr-bot]

🦄 change detected

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Package	Version
gradio	patch
gradio_client	patch

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Attach cookies to client after first request (to support multiple-replica setups with cookie-based affinity)

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[aliabid94]

not sure if we have a way to test this yet
Not yet, but when I add a kubernetes-in-docker docker-test (soon hopefully), you can add a test then