Adding icloud email to Mail app on iPhone 16

I have used a gmail address for my Apple account since I signed up. I also created a mobileme account when those were used. I believe that my old me.com account was migrated to my icloud.com email address, which uses the old mobileme password. In other words, I have two different passwords for my Apple account (the old Apple ID), and for my iCloud email. (My iCloud account uses the password for my Apple account).

When I initially set up my iPhone, I used my gmail mail account for the Mail app. I use the Mail app on my Macbook Pro to access both my gmail and my iCloud emails. I am trying to set up the Mail app on my iPhone 16 to include the iCloud account, but I cannot get it to work. When I go the Mail app on the iPhone 16, I click on Accounts, and then click on iCloud. Then, I get a "choose your email address" page. There is no option for me to access my current iCloud email address. The same thing happens when I click on Add Account.

Any suggestions? Thank you.