I fix the issue by setting the Auth Platform using the "old experience".

I have been using the "new experiencie" (new UI) but couldn't make it work.

Once I followed all the steps in the old experiencie, I was instantly able to create the Clients for Android and iOS.

Don't know if it is a Google issue or what, but as I said, I set up all the required information (following the documentation) which was correctly verified by Google.