Refactoring the playground component

[whitphx]

Description

This is not for a specific issue, but just a refactoring what I found during another work.
By using { BaseCode } instead of Code exported from @gradio/code, we can remove some boilerplates.

[gradio-pr-bot]

🪼 branch checks and previews

•	Name	Status	URL
	Spaces	ready!	Spaces preview
	Storybook	ready!	Storybook preview
🦄	Changes	detected!	Details

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Install Gradio from this PR

pip install https://gradio-builds.s3.amazonaws.com/18469477e2658fca96cfe14517b08b8da89a2fef/gradio-4.37.2-py3-none-any.whl

Install Gradio Python Client from this PR

pip install "gradio-client @ git+https://github.com/gradio-app/gradio@18469477e2658fca96cfe14517b08b8da89a2fef#subdirectory=client/python"

Install Gradio JS Client from this PR

npm install https://gradio-builds.s3.amazonaws.com/18469477e2658fca96cfe14517b08b8da89a2fef/gradio-client-1.2.1.tgz

[gradio-pr-bot]

🦄 change detected

This Pull Request includes changes to the following packages.

Package	Version
@gradio/app	minor
gradio	minor

• Maintainers can select this checkbox to manually select packages to update.

With the following changelog entry.

Refactoring the playground component

Maintainers or the PR author can modify the PR title to modify this entry.

Something isn't right?

• Maintainers can change the version label to modify the version bump.
• If the bot has failed to detect any changes, or if this pull request needs to update multiple packages to different versions or requires a more comprehensive changelog entry, maintainers can update the changelog file directly.

[whitphx]

This conflicts with #8693, so will close this for now and create another PR after #8693 is merged.