@eeeee my mistake, only brand:favicon is used as the favicon.
As you assumed, the touch icon is used for mobile devices. We expose it in the page meta tags as an optional icon for mobile devices to use in bookmarks and when added to the home page.
The "maskable" icon is meant to be an image that is preferable to be edited computationally. An One example of a maskable icon used would be the icons in your phone's notification bar — they're shrunken down and flattened to black-and-white. Some sites would prefer a different icon (maybe one that is less busy, or fewer colours, etc).
For example, on another site I admin, OpenBeta, the icon is white-on-orange. When automatically masked, the icon ends up white on white, which is undesirable, so this site uploaded a black-on-white "maskable icon" that shows up correctly when masked.