### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
for (int i = 0; i < plugins_list.size(); i++) {
		plugins_list[i]->make_visible(p_visible);
	}
}
void EditorPluginList::edit(Object *p_object) {
	for (int i = 0; i < plugins_list.size(); i++) {
		plugins_list[i]->edit(p_object);
	}
}
bool EditorPluginList::forward_gui_input(const Ref<InputEvent> &p_event) {
	bool discard = false;
	for (int i = 0; i < plugins_list.size(); i++) {
		if (plugins_list[i]->forward_canvas_gui_input(p_event)) {
			discard = true;
		}
	}
	return discard;
}
EditorPlugin::AfterGUIInput EditorPluginList::forward_3d_gui_input(Camera3D *p_camera, const Ref<InputEvent> &p_event, bool serve_when_force_input_enabled) {