With the help of Satomi Uematsu (thanks for that!) I found the offline-capable version of the HTML Snippet widget.
I added that to my custom (phone) login page with the suggested javascript.
if(('localStorage' in window) && (window.localStorage !== null)) {
delete window.localStorage.session;
} else {}
if(('sessionStorage' in window) && (window.sessionStorage !== null)) {
sessionStorage.clear();
window.sessionStorage.clear();
} else {}
Using an anonymous login page with the default authentication widgets (7.11) it is not needed to use the login-form widget from the appstore or it's offline capable version.
Then I (re) enabled anonymous use of the app and now it functions as expected.
Ready for the next challenge...understanding the synching to and from the server data....