I am running into this again. I get the misleading error message when I attempt to update the email address a user has an sms identity and not an email identity. You can check this user for yourself. This request fails as it should, but the error message does not make sense. It says the connection does not exist when really the identity does not exist. See the screenshot.
The connection exists, we use it all the time. I can provide a link to the user if needed.
Having looked closely at your screenshot, I noticed that your user is of the Passwordless type, specifically, using sms. This can be seen from the user_id prepended with sms.
Whereas the Username-Password-Authentication connection is a database connection for password users. To clarify, your users should be only of one type and not both at the same time.
I can agree that the error is vague and misleading. I will have to look deeper to find the exact code for why this error occurs for this condition.
Now, to update your Passwordless users, you will want to specify the connection as "sms" and remove the email property since that is irrelevant and will throw an error. See below.