Composer update / upgrade fails

Hello together, using the “new” composer way I always crashing my installation when trying to upgrade a release. What’s the best and tested documentation on upgrading an existing composer installation?

I came from a “converted Mautic” installation, but now installed it via composer from scratch. Its version 4.4.6 that got installed. I wonder, why there is an “app” directory in the base and docroot folder? The one in the base folder is empty.