Thanks for responding. Here are more details on my situation. I'm starting my app and everything is OK so far. Depending on where I am either my local WiFi is being used or cellular. Now I'm attaching the diagnostic WiFi adapter to the car, use Settings -> WiFi to connect to its network and now the following happens:
The iPhone gets an IP, a subnet mask, and – sadly – a router, e.g. 192.168.16.103 / 255.255.255.0 / 192.168.16.254. Interestingly, for a short time, iOS seems to detect that with these settings, there is no internet available, hence it – sometimes – shows the [No Internet Connectivity] subtitle.
Despite all that, the path stays the same as NWPathMonitor still reports 2022-06-03 08:51:42.503 [none:ObservableReachability] <2> (D) Network Path now satisfied (Path is satisfied), interface: en0, ipv4, dns
So at this point of time, I have no internet connectivity.
Now if I manually go into the WiFi settings, change it to 'custom' and set 192.168.16.103 / 255.255.255.0 / (empty router), everything immediately starts to work. In the statusbar, there is 'LTE' and I can connect both to the 192.168.16.x and to the internet.
Now really I can't put the burden to my end users to go in their network settings and do the same I did. That's why I'm begging for a better solution.