If you want to leave Zenless Zone Zero without risking losing your saved data, it's best to find out where the exit is as soon as possible.
21 Final Tips for the Mid-Game | Zenless Zone Zero
Much like exiting Elden Ring or Dark Souls, ZZZ’s logout option is hidden in the depths of the menu screen. If, like me, you’re running for the exit when a player invades my world in Dark Souls, you might not reach the exit button in time. Unlike Souls games, however, ZZZ doesn’t throw anything scary your way to make a quick exit seem like the only viable option. But you’ll probably want to exit the game properly rather than closing it on desktop or mobile.
Here's how to close ZZZ without losing your progress.
To leave ZZZ, click More on the main menu and then click Sign Out. However, this option is not immediately available.