Fix the responsive issue for playground page

[saikatsarkar056]

Summary

The playground page isn’t responsive when the window is resized. This PR fixes the issue by setting a minimum width for the playground body section.

Before

After

Screen.Recording.2025-10-30.at.1.56.19.PM.mov

Checklist

Check the PR satisfies following conditions.

Reviewers should verify this PR satisfies this list as well.

• Any text added follows EUI's writing guidelines, uses sentence case text and includes i18n support
• Documentation was added for features that require explanation or tutorials
• Unit or functional tests were updated or added to match the most common scenarios
• If a plugin configuration key changed, check if it needs to be allowlisted in the cloud and added to the docker list
• This was checked for breaking HTTP API changes, and any breaking changes have been approved by the breaking-change committee. The release_note:breaking label should be applied in these situations.
• Flaky Test Runner was used on any tests changed
• The PR description includes the appropriate Release Notes section, and the correct release_note:* label is applied per the guidelines
• Review the backport guidelines and apply applicable backport:* labels.

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[mdefazio]

Looks good. Thank you!

[elasticmachine]

💛 Build succeeded, but was flaky

• Buildkite Build
• Commit: 1eb7489

Failed CI Steps

• FTR Configs #30

Metrics [docs]

Async chunks

Total size of all lazy-loaded chunks that will be downloaded as the user navigates the app

id	before	after	diff
searchPlayground	235.3KB	235.3KB	-4.0B

cc @saikatsarkar056