Delete @icloud.com mail without deleting the whole Apple ID account

I believe you are referring to the user name you use for the iCloud Mail aspect of your Apple account. You cannot change the primary name you chose. You can, however, use aliases if you still wish to use the mail service but not use the primary user name associated with the account.

Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support - "An email alias is an email address that conceals your actual email address from a recipient. An alias can help you manage the email you receive, and monitor the sources of unwanted messages. You can both send and receive email from an email alias using Mail on iCloud.com.

"With iCloud Mail, you can have up to three active email addresses, and you can turn an email alias on or off at any time. You can also delete email aliases that you no longer want to use. While turning off an email alias is temporary, deleting it is permanent. "

"Note: You can’t delete or turn off a primary iCloud Mail address. You can’t use an alias to create a separate Apple ID, and an email alias can’t be converted to a primary iCloud Mail address."

An Apple ID is an email address, either at Apple or elsewhere. (That didn’t used to be the case, but it's been how things work for the past fifteen years or so.)

Here is how to change the email associated with an Apple ID: Change your Apple ID - Apple Support

Using that, you will switch the Apple ID to your Google address, if I correctly understand your goal.

If that doesn’t work, contact Apple Support and discuss what you want to do, what you’ve tried, and what happened.