How do I report an issue with home internet mobile app?

You would probably be better off opening a trouble ticket with T-Mobile and reporting what you have seen and have to repeatedly deal with. T-Mobile might scrape the information from the community conversations but I sort of doubt they dig that deep here. I have had nothing but problems with the T-Mobile home internet application on my iPhone 12 Pro and I have seen some references here and there about how the application works on an Apple vs. Android device so another report does not surprise me in any way. You should probably also include more specifics about the Manufacturer of the phone, the model of the phone, the firmware/software version it runs etc… It might be helpful for a developer especially since they have to debug issues it helps to be able to reproduce them. I find the mobile application for gateway management to be nothing but a bother so I am extremely happy to still have the Nokia gateway as I don't have the frustration of trying to manage a network appliance with a mobile device. The web GUI rules for management of the gateway in my opinion. The decision to force the flakey mobile application upon users is a very poor one. I am sure it was only driven by the bean counters. 

One suggestion I can make with respect to the behavior you are talking about. When you see the gateway shows it has cellular communication go to a client on the local network and then change its DNS to say google.com 8.8.8.8 or 8.8.4.4 or quad9 9.9.9.9 or CloudFlare 1.1.1.1 and then see if that client can communicate to the internet. I have seen times when my gateway shows the cellular communication and I can see the inbound and outbound counters incrementing but have clients report no internet. If you change the DNS from 192.168.12.1 to one of the public hosted DNS servers and it works it just proves there is a DNS issue not some other problem with the gateway. It might save you from rebooting the gateway. Another tactic might be to flush the DNS from the client and try again but if the DNS is not resolving from the gateway router interface then it has stale information or is not communicating with the upstream authoritative DSN server.