If you get a new phone and want to be able to sign into your existing iCloud account, then you will need to use the same Apple ID as before. And, you'd likely end up where you are now. See if these document on two-factor authentication help you.
Two-factor authentication for Apple ID https://support.apple.com/en-us/HT204915
Get a verification code and sign in with two-factor authentication https://support.apple.com/en-us/HT204974
“Whenever you sign in with your Apple ID on a new device or browser, you'll confirm your identity with your password plus a six-digit verification code. There are a few ways you can get a verification code. You can use the code displayed on your trusted device, get a text or phone call, or generate a code from your trusted device.
If you didn't receive your verification or reset email https://support.apple.com/en-us/HT201455
“Not sure where that email was sent? Here are some tips to help you find it. When you make certain updates to your Apple ID, we’ll send you an email to help youcomplete the update. For example, you might have [a] reset your password, [b] reset your security questions, or [c] added a new email address to your account.
