[core] Use `hidden` prop for `keepMounted` elements

[atomiks]

• [x] I have followed (at least) the PR section of the contributing guide.

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Popup animations: https://deploy-preview-815--base-ui.netlify.app/experiments/tooltip

• Prevents the need to apply CSS to use keepMounted by default
• Styling animations is now the same as conditional rendering, so it's overall more consistent. They need to use [data-entering] and wait 1 frame as well, once hidden gets removed on open
• inert is no longer necessary for these components
• Fixes anchor positioning performance for keepMounted components, both on initial mount and for the lifetime of the mount

[mui-bot]

Netlify deploy preview

https://deploy-preview-815--base-ui.netlify.app/

Generated by :no_entry_sign: dangerJS against a6c9ab00e41e3846ec4838f23f0d2eaf555dee72

[michaldudak]

Dialog and AlertDialog were not updated. The rest looks OK.