Replace DevTools mutable Suspense cache with newer Cache API

[bvaughn]

Follow up to PR #20463 and 5d10e41

It would be nice to replace the outdated cache API currently used in DevTools with a newer one that's compatible with APIs like useTransition. This would allow DevTools to better handle UX like clearing errors/warnings for the inspected element without needing to immediately poll for new data. (Currently it's either that or show an awkward second or two delay after you click the button before anything appears to happen.)

[github-actions]

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[github-actions]

Closing this issue after a prolonged period of inactivity. If this issue is still present in the latest release, please create a new issue with up-to-date information. Thank you!