Application up and running but not shown in Console Management

Hello.

Is it possible that you are accessing a different AWS account or a different region?
Please try changing the region of the management console using the steps described in the following document.
https://docs.aws.amazon.com/awsconsolehelpdocs/latest/gsg/select-region.html

I cannot even find any way to connect to any support from aws to get the amplify application down.

AWS Support can be accessed from the following URL.
https://support.console.aws.amazon.com/support/home#/

I agree that you should confirm that you're in the same AWS account and region where the Amplify resource was initially created. This is most likely to be where the issue lies.

If you were just starting to learn AWS at the time the resource was created, chances are that you may have created it in the default region.

Another tool you can use to find out if the service is still running is Cost Explorer. It will indicate all your active services. However, to access it, you'll need to sign in as the root user.