Unable to add iCloud email account to Mail on Mac

I have tried a number of times to add an iCloud email account used by my wife on her iPhone 16e to our Mac’s Mail.   I thought it would be straightforward as my own iPhone 16e’s iCloud email account is on the Mac already, as well as another shared email account with an ntlworld address.

This is what happens:

I opened Mail.

I selected Add Account and was then offered a choice of iCloud, Microsoft Exchange, Google, Yahoo, AOL, or other.

I selected iCloud and clicked Continue. 

I signed in to iCloud using my Apple ID and password.

I was then presented with System Settings, Internet Accounts.

I clicked on Add Account and was presented with the same choice as in step 2 above.  

I was then requested to sign into iCloud as in step 5 above.

I signed in with ID and password, and was presented with System Settings, Internet Accounts, which does not offer an obvious option of adding another account to Mail.  

I selected Internet Accounts, and then Add Account.

When I entered the account name and password I get the message - “Unable to verify account name or password”.

I'm aware another user sought help back in 2022 when trying to add a Microsoft email account. But all I'm trying to do is add another Apple iCloud email account.

My Mac is a 2017 Retina 5K, 27 inch.  Software is Ventura 13.7.8.

Can you please help me?  Apologies if I've missed something obvious.

Thank you.

Callum D.