Improve UI for lazy caching

[abidlabs]

When examples were cached, we previously combined two events together: loading the input value and loading the output value. For eager caching, this makes sense, but for lazy caching, we should first load the input value (since that's instantaneous) and then load the output value, which can be time-consuming.

Closes: #10866

[gradio-pr-bot]

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Install Gradio from this PR

pip install https://gradio-pypi-previews.s3.amazonaws.com/38ad2931e0b4361bfa8b255ab64c235c3b62020c/gradio-5.23.0-py3-none-any.whl

Install Gradio Python Client from this PR

pip install "gradio-client @ git+https://github.com/gradio-app/gradio@38ad2931e0b4361bfa8b255ab64c235c3b62020c#subdirectory=client/python"

Install Gradio JS Client from this PR

npm install https://gradio-npm-previews.s3.amazonaws.com/38ad2931e0b4361bfa8b255ab64c235c3b62020c/gradio-client-1.14.0.tgz

Use Lite from this PR

<script type="module" src="https://gradio-lite-previews.s3.amazonaws.com/38ad2931e0b4361bfa8b255ab64c235c3b62020c/dist/lite.js""></script>

[gradio-pr-bot]

🦄 change detected

This Pull Request includes changes to the following packages.

Package	Version
gradio	patch

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Improve UI for lazy caching

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[abidlabs]

I think this should also close: #10362, @hysts can you confirm?

[hysts]

Thanks! But it seems that #10362 still persists.
As there's another issue #6690 related to gr.Progress and gr.Examples, #10362 might be a bit different issue from the one this PR resolves.

[abidlabs]

Ok thanks for confirming @hysts!

[aliabid94]

LGTM!

[freddyaboulton]

Verified + looks good @abidlabs

[abidlabs]

Thanks folks!