Update the PageSpeed Insights widget to use badges for performance ratings.

## Feature Description

Once #13361 is implemented, we should update the dashboard's PageSpeed Insights widget to show badges for performance ratings instead of text labels.

The [PDF version of the widget](https://www.figma.com/design/fwNvz1r40HJk2FpqBUhDme/PDF-report-generation?node-id=1087-8262&t=6en9yS3YWjrvHMoj-0) already uses badges and can serve as a reference.

Note that a performance rating may show in a gathering data state, in which case the gathering data badge should be used.

See this [thread](https://www.figma.com/design/ZL8qlbUyR9lmBaF95t0xpq/sitekit-system-gm2-?node-id=388-422#1885637437) on Figma.

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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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Start with the dashboard's PageSpeed Insights widget and compare its current performance-rating labels with the badges used in the PDF version of the widget. Review the linked Figma designs and the dependency on issue #13361, then update the rating display so gathering-data states use the gathering data badge and verify the other ratings match the designs.

Written by the indexing model from the issue text.