Hello colleagues. I was able to remember what problem could lead to this behavior.
Some time ago (about a month before the problem with mobile login was discovered) on the reverse proxy server (Windows server 2019+IIS ARR) the Default application pool stopped running.
The error was of the form: "A listener channel for protocol 'http' in worker process '#' serving application pool 'DefaultAppPool' reported a listener channel failure. The data field contains the error number." Event ID 5139, WAS
Some time later I accidentally discovered that if I change the Identity of the App pool from "ApplicationPoolIdentity" to Local system, the pool stops crashing and works. At this point, I calmed down, but the root cause of this behavior was this. I eventually failed to get the pool to start under Identity "ApplicationPoolIdentity", so I simply re-deployed the server and reconfigured it.
It is important that the DefaultApplicationPool should work with Identity "ApplicationPoolIdentity".
Right now, everything works fine -my problem was solved.
Maybe my answer will help someone with the same problem and save a lot of time.