Function write_pointer_button_messages_system 

pub fn write_pointer_button_messages_system(
    egui_global_settings: Res<'_, EguiGlobalSettings>,
    commands: Commands<'_, '_>,
    modifier_keys_state: Res<'_, ModifierKeysState>,
    mouse_button_input_reader: EguiContextMessageReader<'_, '_, MouseButtonInput>,
    egui_input_message_writer: MessageWriter<'_, EguiInputEvent>,
    egui_contexts: Query<'_, '_, (&EguiContextSettings, &EguiContextPointerPosition), With<EguiContext>>,
)

Reads MouseButtonInput messages and wraps them into EguiInputEvent, can redirect messages to HoveredNonWindowEguiContext, inserts, updates or removes the FocusedNonWindowEguiContext resource based on a hovered context.