### 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
if (EDITOR_GET("interface/editor/separate_distraction_mode")) {
		int screen = -1;
		for (int i = 0; i < editor_table.size(); i++) {
			if (editor_plugin_screen == editor_table[i]) {
				screen = i;
				break;
			}
		}
		if (screen == EDITOR_SCRIPT) {
			script_distraction_free = !script_distraction_free;
			set_distraction_free_mode(script_distraction_free);
		} else {
			scene_distraction_free = !scene_distraction_free;
			set_distraction_free_mode(scene_distraction_free);
		}
	} else {
		set_distraction_free_mode(distraction_free->is_pressed());
	}
}
void EditorNode::set_distraction_free_mode(bool p_enter) {
	distraction_free->set_pressed(p_enter);
	if (p_enter) {
		if (docks_visible) {
			set_docks_visible(false);
		}
	} else {
		set_docks_visible(true);
	}
}
bool EditorNode::is_distraction_free_mode_enabled() const {