The answer is easy and not easy. After several hours of debugging with Appsheet support and consulting a specialist, I received the following answer:
"We have got an update from our specialists and we got to know that the app won’t show in the shared with me section because it is not shared directly with the user. It’s not the same as sharing apps with the domain.
AppSheet can only recognize those apps which are directly shared with the users. You can only use the apps when shared via domain authentication but the app itself is not shared with users so they are not able to see in the gallery."
After further testing I discovered you can start your app through the gmail link, also in the Appsheet app. But Appsheet crashes when you visit the App Gallery, as Shared with me shows nothing. After quitting and restarting Appsheet, it automatically opens your app.
What I wanted to achieve is shared my app with a Google Workspace group through Domain Authentication. If you do it this way, it works as described above.
The only way to get your app showing up in Appsheet is to add all the email addresses of the individual users of your group in the “Share app” pop-up menu. You also can enter in this menu your domain name in the form domain.extension, in this case all the users in your domain will see your app in the App Gallery.