Switching to existing Gmail account.

Understandable. You should not need to create a new iCloud email address nor do I recommend it.

Review Change your Apple Account primary email address - Apple Support

A cursory read suggests you're doing it right, but review the above and let us know what is not working. For example you have to de-select Primary Email first. Assuming you did that, describe what happens next.

Please do not divulge your email address(es) over this site because it is publicly viewable.

It is not clear to me what you mean by an "iPhone account". There are all sorts of accounts on an iPhone — Apple Accounts, email accounts... etc.

If you were to provide the steps, perhaps someone else could follow along and understand what you are trying to do.

If you want to add an existing Google Mail account to the Mail app, follow these steps: Add an email account to your iPhone or iPad - Apple Support

I am trying to change the primary email address associated with my Apple Account to my existing Gmail address. I do not want to create a new @icloud.com email address.

On my iPhone, I went to Settings → [my name] → Sign-In & Security and attempted to delete/remove my current primary email address. However, when I proceed with changing the primary email, the only option I am being given is choosing a new iCloud email address. The screen requires me to create an @icloud.com address.

I am not being given an “Existing Email Address” option or any field where I can enter my existing Gmail address.

My goal is simply to have my existing Gmail address become the primary email/sign-in address for my Apple Account, rather than creating a new iCloud email address.

I reviewed the link and followed the steps outlined there. Also, I have already de-selected my existing @icloud.com email address as the Primary Email and successfully added my Gmail address as the new Primary Email.

The issue is what happens after that. Although Gmail is now shown as my Primary Email, the existing @icloud.com address remains associated with my Apple Account and can still be used to sign in. I am trying to completely remove that @icloud.com address from the account so that my Gmail address is the only email address associated with and used for my Apple Account.

When I try to remove the @icloud.com address, however, I am taken to the “Choose New iCloud Email Address” screen and am only given the option to replace it with another @icloud.com address. I am not given an option to remove the iCloud address altogether.

Is there a way to completely remove the existing @icloud.com address without replacing it with another iCloud address, so that my Gmail address is used for my Apple Account going forward?

I reviewed the link and followed the steps outlined there. Also, I have already de-selected my existing @icloud.com email address as the Primary Email and successfully added my Gmail address as the new Primary Email.

The issue is what happens after that. Although Gmail is now shown as my Primary Email, the existing @icloud.com address remains associated with my Apple Account and can still be used to sign in. I am trying to completely remove that @icloud.com address from the account so that my Gmail address is the only email address associated with and used for my Apple Account.

When I try to remove the @icloud.com address, however, I am taken to the “Choose New iCloud Email Address” screen and am only given the option to replace it with another @icloud.com address. I am not given an option to remove the iCloud address altogether.

Is there a way to completely remove the existing @icloud.com address without replacing it with another iCloud address, so that my Gmail address is used for my Apple Account going forward?

Although Gmail is now shown as my Primary Email, the existing @icloud.com address remains associated with my Apple Account and can still be used to sign in.

Correct. It will always be so.

Unless...

I am trying to completely remove that @icloud.com address from the account so that my Gmail address is the only email address associated with and used for my Apple Account.

In that case please review How to delete your Apple Account - Apple Support. In doing so, be sure to exercise the utmost care.

I reviewed the link and followed the steps outlined there. Also, I have already de-selected my existing @icloud.com email address as the Primary Email and successfully added my Gmail address as the new Primary Email.

The issue is what happens after that. Although Gmail is now shown as my Primary Email, the existing @icloud.com address remains associated with my Apple Account and can still be used to sign in. I am trying to completely remove that @icloud.com address from the account so that my Gmail address is the only email address associated with and used for my Apple Account.

When I try to remove the @icloud.com address, however, I am taken to the “Choose New iCloud Email Address” screen and am only given the option to replace it with another @icloud.com address. I am not given an option to remove the iCloud address altogether.

Is there a way to completely remove the existing @icloud.com address without replacing it with another iCloud address, so that my Gmail address is used for my Apple Account going forward?

I reviewed the link and followed the steps outlined there. Also, I have already de-selected my existing @icloud.com email address as the Primary Email and successfully added my Gmail address as the new Primary Email.

The issue is what happens after that. Although Gmail is now shown as my Primary Email, the existing @icloud.com address remains associated with my Apple Account and can still be used to sign in. I am trying to completely remove that @icloud.com address from the account so that my Gmail address is the only email address associated with and used for my Apple Account.

When I try to remove the @icloud.com address, however, I am taken to the “Choose New iCloud Email Address” screen and am only given the option to replace it with another @icloud.com address. I am not given an option to remove the iCloud address altogether.

Is there a way to completely remove the existing @icloud.com address without replacing it with another iCloud address, so that my Gmail address is used for my Apple Account going forward?