Update the design of the PageSpeed Insights widget's "gathering data" state

## Feature Description

As discussed on [Slack](https://10up.slack.com/archives/C01CA828ZPZ/p1705579990757279?thread_ts=1705486654.225629&cid=C01CA828ZPZ), we are going to update the design of the PageSpeed Insights widget to improve the "gathering data" state.

@sigal-teller will provide an updated design; this could potentially reuse the "partial data" badge styling from the Audience Segmentation feature.

This issue follows on from https://github.com/google/site-kit-wp/issues/7685.

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## Acceptance criteria

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## Implementation Brief

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### Test Coverage

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## QA Brief

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## Changelog entry

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