I think you're confusing what it is asking for. I have never, ever in 20 years had Apple ask for the password to my email account.
The support article Change your Apple Account primary email address - Apple Support outlines various methods for changing the email address (Apple ID) you use for your Apple Account while retaining everything in your account.
If you have an older iOS/iPadOS, Apple no longer provides the instructions for that, but here they are:
1. Go to Settings, then tap your name.
2. Tap Sign In & Security.
3. Next to Email & Phone Numbers, tap Edit.
4. Tap the red Remove button next to the email address, then tap Delete.
5. Tap Choose Another Email Address and enter your device passcode if asked.
6. Enter the new email address, then tap Continue.
7. Enter the verification code that was sent to your new email address. Read this support article to learn what to do if you didn’t get the email —> If you didn’t receive your verification or reset email - Apple Support
8. If you encounter issues with certain services after doing this, this outdated support article may still have useful suggestions --> What to do after you change your Apple ID or password - Apple Support
Also do not confuse changing the email address used with your Apple Account with instead setting up a second account. You do NOT want to set up a second account unless you really know what you are doing.