Reporting same issue: no notifications in Delta Chat 1.36.4 under iOS 16.5. Server Dovecot, push enabled. This was tested on several iPhone and iPad devices with same results.
There are multiple support and github threads previously closed, reporting same issue. Not clear why they were closed though as same issue remains unresolved. This renders the app useless as a Chat tool. The suggested AppleMail workaround is not feasable.