### 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 (get_edited_scene()) {
		if (current_tab < 2) {
			Node *editor_node = SceneTreeDock::get_singleton()->get_tree_editor()->get_selected();
			editor_node = editor_node == nullptr ? get_edited_scene() : editor_node;
			if (Object::cast_to<CanvasItem>(editor_node)) {
				editor_select(EDITOR_2D);
			} else if (Object::cast_to<Node3D>(editor_node)) {
				editor_select(EDITOR_3D);
			}
		}
	}
	if (p_state.has("scene_tree_offset")) {
		SceneTreeDock::get_singleton()->get_tree_editor()->get_scene_tree()->get_vscroll_bar()->set_value(p_state["scene_tree_offset"]);
	}
	if (p_state.has("property_edit_offset")) {
		InspectorDock::get_inspector_singleton()->set_scroll_offset(p_state["property_edit_offset"]);
	}
	if (p_state.has("node_filter")) {
		SceneTreeDock::get_singleton()->set_filter(p_state["node_filter"]);
	}
	
	EditorDebuggerNode::get_singleton()->update_live_edit_root();
	ScriptEditor::get_singleton()->set_scene_root_script(editor_data.get_scene_root_script(editor_data.get_edited_scene()));
	editor_data.notify_edited_scene_changed();
	emit_signal(SNAME("scene_changed"));
	
	RenderingServer::get_singleton()->sdfgi_reset();
}
bool EditorNode::is_changing_scene() const {