Update playwright - 6.5 branch

[desrosj]

The E2E and Performance testing workflows have started failing recently for branches using Playwright. This seems to be due to the change for ubuntu-latest to now point to ubuntu-24 instead of ubuntu-22.

Updating Playwright to the latest version seems to fix the issue with no obvious side effects. Since this only effects build tooling and not the built software, this seems like a reasonable change to make in a somewhat older branch.

• 6.5 branch failing E2E workflow
• 6.5 failing performance workflow

See also #8169, #8164, #8164, #8171.

Trac ticket: https://core.trac.wordpress.org/ticket/62843

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[github-actions]

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Props desrosj.

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[github-actions]

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Test this pull request with WordPress Playground.

[desrosj]

Fixed in https://core.trac.wordpress.org/changeset/59685