The behaviour you have pointed out is an expected one. As you are trying to connect RDP into instances using Fleet manager on one-click authentication with SSO, the authentication will be done in the region where IAM Identity Center(SSO) is enabled. Therefore, you will not be able to view the option to select authentication type as SSO in the regions where SSO was not enabled. On this note, please allow me to remind you that IAM Identity Center is only supported in one AWS region at a time.
If you're authenticated to the AWS Management Console using AWS IAM Identity Center, Fleet Manager integrates with AWS IAM Identity Center so you can connect to your instances without providing additional credentials. Fleet Manager supports AWS IAM Identity Center authenticated RDP connections in the same AWS Region where you enabled AWS IAM Identity Center
 AWS IAM Identity Center (successor to AWS Single Sign-On) Region availability - IAM Identity Center Region data - https://docs.aws.amazon.com/singlesignon/latest/userguide/regions.html#region-data
 Connect using Remote Desktop - https://docs.aws.amazon.com/systems-manager/latest/userguide/fleet-rdp.html
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