This may not be clear to you from the documentation states:
If the instance of SQL Server is running under a domain account and
the password for that account is changed, the password used by SQL
Server must be updated to the new password.
This implies that you have to change the password in Active Directory first and then follow that procedure to update the SQL Server service account password using Configuration Manager.
As long as the service is running it will keep running after you change the password in Active Directory, but it will need the new one the first time it restarts.
Trying to change the password in Configuration Manager before it's changed in Active Directory will result in a failure to start the service as the account won't be able to authenticate.
Your credential will need to be changed after changing the password in Active Directory and isn't really related to when you change your service account password. You could do the credential first and the service account second or the other way around, as long as you change it in Active Directory first.
Changing the service account or the credential account will have no impact on one another. Updating one won't change the other and you have to change both yourself.