I am sure users would simply love that. The point of sign in with Apple is that I don’t have to give out my real email. If you ask me for it anyway, I’m gone.

Users already do that with many sign up flows now. We are talking about a button press + an auto filled email field, doubt conversions would plummet.

What information would you gain from sending a test email? Wouldn't test emails sent to Apple's anonymous forwarding email also go through?

There's really no such thing as checking for a "real" email address, though lots of sites do blacklist known anonymous email domains like 10minutemail. But nothing can stop you from just signing up for a new Gmail.

Senders to Apple's email proxy needs to be pre-registered first (and I highly suspect the generated addresses are scoped to each individual app's whitelist), so no, not everyone can send to those addresses.

The sender already is pre-registered. We're talking about users who have successfully Signed In With Apple ID.

After signing up you would request a non proxy email. Hence, the “real” email. You would then test that the user supplied email is legit.

But nothing is stopping the user from supplying a proxy email address in your textbox where you ask for a non-proxy email address. Sending a test email doesn't tell you whether the user-supplied email address is a proxy email address or a non-proxy email address, since your test email will go through in either case. That's the whole point of a proxy email address instead of a completely fake email address, is that emails sent to the proxy email address will still go through.

I imagine if you did you would be swiftly (hah) kicked out of the App Store