Hi, @Christoph_G.
When you a create a custom connector configured with an authentication type of generic Oauth 2.0, Oauth 2.0 for specific services or Basic authentication, by default the PowerApp user will be prompted to provide credentials so the app can create a connection.
A custom connector with authentication type 'API Key' won't prompt the end user for credentials. The authentication details are specified when creating an app that uses this type of connector, when the app is shared the connection already exists and end users won't be prompted for creds.
The authentication types that can be defined in a custom connector are outlined here.
Also, an easy way to confirm if a connection is automatically shared with app users is outlined here.
Lastly, there is one more alternative to the info above, when you create a connection for your app using basic auth you can share the connection with the same users the app is shared with. Note, basic auth connections are not implicitly shared with users when an app is shared with them. For instance, go to https://make.powerapps.com > Data > Connections > Select the connection you created for the app to be shared > In the details pane of the connection there is a 'share' button.