There are several places to turn them on or off depending on what settings you have set for the addon. The viewport gizmos dropdown should be visible no matter what settings you have set, as long as the header isn’t hidden in the 3d View.
None of these locations should disappear when you switch to sculpt mode.
Depending on how you have your keymap set up, you may not be able to access the functionality through keymaps in sculpt mode. Keymap entries can either be mode dependent or workspace dependent.
If none of these are convenient, the default Blender keymap for toggling gizmo visibility is CTRL+~ on a North American keyboard, but I think that one key varies depending on what language keyboard you have.