I modified your reply to remove any personal information. This forum is public so be careful posting personal information here.
With that said, a few things we need to confirm:
ATM (Adobe Tag Manager) has been deprecated and was replaced by DTM (Dynamic Tag Manager) years ago. Are you trying to log into ATM or DTM?
The login link you provided was on the my.omniture.com domain. This URL is only used to log directly into Analytics. To log into DTM, you'll need to either log into marketing.adobe.com or dtm.adobe.com depending on your implementation of DTM.
If you're trying to sign in with your Creative Cloud credentials, you'd need to log in via marketing.adobe.com since they would be either an Adobe ID, Enterprise ID, or Federated ID. Logging in via dtm.adobe.com does not support any of those credentials
Finally, I don't see either of the email addresses you provided (firstname.lastname@example.org & email@example.com) listed as users in the DTM interface. It seems like you still need to have your Adobe Cloud admin grant you access to DTM.
What Jantzen said on this one. If you need help PM either myself or Jantzen and either one of us can go into your Org and we can help you out here. Likely though its just missing a user group. Depends on how DTM is handling the permissions if its running with it by itself then you have to have someone add you that way to access. If you are using it with the Cloud then depends on what permission group you were given. DTM in the Cloud you can really only belong to one user group so if there are multiple that will also cause the same thing.
Example: If I belong to Admins and Approvers both at the same time DTM has a hard time determining the access so instead you will get a message that you cannot get into DTM.
For though what you are describing it almost sounds to me without the screen shots here to see since those were removed that perhaps this could be a problem with the landing page which I saw one of these recently. IMS SSO error was the error message from Analytics caused by not SSO but the permission state between the Cloud and Analytics not being able to read in the permissions at first login fast enough so instead it tosses an error. If this is happening send me a PM happy to give you a hand here see what we can address for you.