Change Apple ID email

Is this what your partner did to change your Apple ID email?

Change your Apple ID - Apple Support

As shown in this article, if your Apple ID is a @iCloud.com email address, you will need to wait 30 days before you can change it back.

It cannot be done in the phone settings or when creating a new Apple ID and can only be done by signing into your Apple ID on the website and changing your email address from there. Since your partner now has a different Apple ID, is it showing your account information and the data that you had saved into iCloud?

If your account info is not showing up under their Apple ID, they may have successfully created their own and there is just another issue of you not being able verify your Apple ID on the new device.

Before giving your device to your partner, the iPhone should have been reset to the factory settings, otherwise there will be problems with Activation Lock as the device will always be tied to your Apple ID along with two-factor authentication that has been set up previously.

How to factory reset your iPhone, iPad, or iPod touch - Apple Support

You should have done the things in this article before giving him your phone What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Change your Apple ID - Apple Support

Apple says: "When you make certain updates to your Apple ID, we’ll send you an email to help you complete the update. For example, you might have reset your password, reset your security questions, or added a new email address to your account." If Apple tries sending you a verification email and you do not receive it, read this support article --> If you didn't receive your verification or reset email - Apple Support

What specific verification requests are you seeing? What is the exact wording of the messages?