> Is it just the 6 digit code that Apple sends to verify iCloud access?

No. It is unrelated to Apple ID 2FA.

If its what I'm thinking of, it used to be a user-visible thing[1] back in the day.

But now with the need for increased security posture in the modern environment it is now not user visible but held locally and encrypted using the local device secure enclave key. So you would typically now see a prompt for the device password so the enclave can be accessed to access the key to setup/renew iCloud access tokens.

As far as I am aware the only user-visible string still available in the Apple world is (for obvious reasons) the FileVault recovery key on macOS devices. Which is only visible once ... shown to you when you first enable FileVault.

[1] https://support.apple.com/en-us/101265

I think it's longer then 6 digits. Long ago I did this and I remember it being a long code with dashes.