Despite my nuki is connected to wifi:
The app keeps showing it disconnected:
How to fix it?
Looks like a server problem at Nuki (again). The work-around that often works is to remove the battery and reinsert it some 30 seconds later.
I do not use WiFi for my Nuki 4.0 but Matter. However, I had problems with the WiFi connection of my Rituals Perfume Genie. This device, like the Nuki, only works with 2.4 GHz. Once I made an extra SSID with only 2.4 GHz, the connection problems with the Perfume Genie were over. Maybe this works for your Nuki as well.