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Some security keys have screens. Trezor supports U2F and displays the request being authorized on the screen, i.e. U2F authentication for a specific site. It has an internal list of the fingerprints for common sites to display a name / icon for sites like Google and GitHub too.
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Setting this up is a different process from setting up the Google prompt and it's a way better choice to add the phone as a security key. It's best on devices with a high quality HSM-based keystore but even with the traditional TrustZone keystore it's way better than the prompt.
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Even a software-based keystore implementation would be a bit better than the Google prompt approach but the hardware-based keystore has been mandatory for a few years so there's no need for that. The prompt is tied to active logins on devices rather than having an actual pairing.
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