@Vero thanks for the swift reply!
With your suggestion I understood and fixed the problem in the end: The login list already contained an "Alfred 4" app which was no longer there since the upgrade (moooonths ago).
After I did that, the checkbox selection was persisted properly and Alfred 5 could add itself again in the Login Item list.
So perhaps it's a good suggestion for Alfred to able to manage that version conflict or warn about what to do manually when it happens.
Thanks a lot!