So, the game just doesn't display any on-screen controls. That's why it's also impossible to complete the tutotorial that appears after launching the game for the first time. It's also impossible to pause the game or quit to the main menu by pressing the "back" button. The tutorial, main menu and the "skip song" message in-game display controller button prompts, specifically PlayStation button prompts. It seems like the game expects controller input despite no controller being connected.
It seems there is a problem with automatic disabling of touch controls. I think there should be an option to manually disable/enable touch controls, if such an option was in the menu, this bug wouldn't be so problematic.