How do you update details of secondary linked accounts?

We have users who have multiple accounts linked (SMS passwordless, email passwordless, username/password, etc).

We have an admin UI which will allow admin users to update the mobile number of a user.

Using the ManagementAPi, I can see I can easily update the mobile number of a SMS passwordless account if it is a primary account, but how do I do this when it is a secondary account?

I did try constructing a userId myself for the secondary account to see if I could use that to do the update, but it says user not found.

Is my only option to un-link the SMS passwordless account first, update it and then re-link it?