Creating Desktop Widgets
The floating menus an also be used as interactive Desktop widgets. On macOS version 13 (Ventura) these are completely handled by BTT. On the (upcoming) macOS version 14 (Sonoma) you will soon have the option to use these widgets as part of the native widget support (this will be supported starting with BetterTouchTool 4.500 - sorry it is delayed).
To make a floating menu into a Desktop widget, just change the "Window Level" property in the menu configuration. If you select "Same as Desktop Icons" it will stick to your Desktop, just like the native macOS Sonoma widgets.
Note: I recommend to first configure your menu with window level "Standard Float On Top". Once you got the positioning and content right, you can change the window level to stick it to the Desktop.