Looks like Nuki Web is conflicting with the OpenHAB 3.2 bridge. I have Opener+Bridge with activated Nuki Web for push notification on my android device. However, after integrating Opener into OpenHAB with callbacks enabled, I stopped receiving push notifications. Sometimes my device vibrates indicating the notifications are coming in but I assume they are cleared immediately.
If I understand your setup correctly, this should be completely indepent of each other. - Except if the OpenHAB keeps the device/bridge so busy for some reason that new log entries are never synced to Nuki Web (which is needed for the push notifications to be triggered).
Best first check therefore is always to see how long the updates in Nuki Web takes,
If those come immediatly and you still see no push notification on your smartphone best try to deactivate and activate them again.
If there are issue you could only test again compared to then you deactivate OpenHAB.