js-packages: Fix some JS lints ahead of the eslint 9 upgrade

[anomiex]

Proposed changes:

To make the eslint 9 upgrade PR smaller, let's fix some of the lints that it'll complain about ahead of time.

Of particular note is that, when we added 'plugin:@wordpress/jsx-a11y' in #38436, we accidentally left 'plugin:jsx-a11y/recommended' in place after it which overrides some of the configuration that 'plugin:@wordpress/jsx-a11y' does. Fixing that disables a few rules we had been inline-ignoring in various places: jsx-a11y/media-has-caption, jsx-a11y/no-noninteractive-tabindex, and jsx-a11y/role-has-required-aria-props.

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Testing instructions:

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[github-actions]

Are you an Automattician? Please test your changes on all WordPress.com environments to help mitigate accidental explosions.

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[github-actions]

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