We use Moodle on our site and have done for 9 years.
Downloaded the app, tried the moodle trial site as a student and was very impressed. I then tried to log out.
After trying every screen and setting I could find, and searching google and moodle, I gave up. The only way I found to log out was to uninstall the app. Surely I must be missing something?
I installed the app on my Pixel 2, which is fully updated.