For privacy reasons, I use a Microsoft Hotmail address for some purposes.

When I log on to it, it displays the account's verification address as an optional method of confirming my ID.

That shows my personal domain, and so would link the address to me, for any attacker trying to log in.

This happens in new private windows, so is not cookie based.

There doesn't seem to be an option to turn it off, or to select the option to verify by password as the default.