Regarding the 2FA, the email verification is probably the most useless thing when it comes to security, if your account is hacked it started with your email, you can always use google authenticator or a security key and you don't depend again on third parties like an email or a mobile data provider.
Binance is using a combination of 2FAs so if OP has their email verified + authenticator app enabled, binance would ask for both of them. Last time I check (months ago), there was no workaround to only use one. Email and SMS 2fa are both insecure anyway, imo they are more likely to provide inconvenience rather than security.
Meanwhile, you can login to your binance.com account by scanning a QR code using the binance app lol.