Recently have noticed that the themes stopped switching. I got stuck on the theme for the desktop.
The server does not show any error messages.
How do I identify the problem?

Try to visit
[yourwebsite.url]/index.php?device=
to run device detection again. If it doesn't change template, try to visit
www.mobilejoomla.com/uatest.php
in your mobile browser to check that it is correctly detected by AMDD detector as a mobile device.

1. www.mobilejoomla.com/uatest.php properly detected mobile device as mobile user-agent (Android 9)
2. Adding /index.php?device= at the end of domain name showing desktop version.
3. The other thing that also not working - cannot disable Mobile in mobile -> general -> settings -> enable mode
Mobile extension is always "enabled". I can disable it only in Joomla extension manager.
Any other settings (when changed) in Mobile seems saved well.
4. I'm also reinstalled the extension and switching off other plugins but without success.

Thanks again for the tips.
The problem was with installed extension Regular Labs Advanced Template Manager
If somebody have the same problem - you have to assign your mobile templates with mobile devices, by default it was switch off.