Apple has their own remote attestation infrastructure and you will not be able to impersonate an Apple device without extracting private key material from the secure enclave of a legitimate Apple device or compromising Apple certificate authority private keys.

Is this actually available in Safari?

Since iOS 16, apparently

https://blog.cloudflare.com/eliminating-captchas-on-iphones-...

https://developer.apple.com/news/?id=huqjyh7k

Can they present themselves as... web browsers?

Yes, and then they'll get served a QR code that you have to scan on a phone Google approves of.

In the UK, the Department of Education guidance is that schools should be mobile-phone free. Students use computers to access the web fairly regularly. Guess that would be problematic then, since many schools policies is that mobile phones should be turned off and stored in your bag during the day.