Mail keeps asking for password to use the "System" keychain.

I have Mail accessing my email account in iCloud, using my own domain. Everything works fine, but every time Mail wants to save a message in drafts, it says:

Mail wants to make changes. Enter an administrator's name and password to allow this.

Mail wants to use the "System" keychain.

I have to do this 3 or 4 times and it goes away, but I need to repeat every time I open Mail.

I read the instructions provided in the same pop up box leading to this article:

Allow apps to access your keychain - Apple Support 

However, I only get the options to "Deny" or "Allow" and I don't see the "Always Allow" option. Moreover, the instructions to configure this manually in the Keychain application don't apply either, since I don't see the app's keychain as instructed: "The app’s keychain is probably in your login keychain"

Having to enter the same user/password 3-4 times in a row every time I launch Mail is not pleasant, and I wonder if there is a way to fix this.

This problem was present in Catalina and continues to exist after the Ventura upgrade.