### 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
file_menu->set_item_disabled(file_menu->get_item_index(FILE_OPEN_PREV), previous_scenes.is_empty());
	_update_undo_redo_allowed();
}
void EditorNode::_update_file_menu_closed() {
	file_menu->set_item_disabled(file_menu->get_item_index(FILE_OPEN_PREV), false);
}
VBoxContainer *EditorNode::get_main_screen_control() {
	return main_screen_vbox;
}
void EditorNode::editor_select(int p_which) {
	static bool selecting = false;
	if (selecting || changing_scene) {
		return;
	}
	ERR_FAIL_INDEX(p_which, editor_table.size());
	if (!main_editor_buttons[p_which]->is_visible()) { 
		return;
	}
	selecting = true;
	for (int i = 0; i < main_editor_buttons.size(); i++) {
		main_editor_buttons[i]->set_pressed(i == p_which);
	}
	selecting = false;
	EditorPlugin *new_editor = editor_table[p_which];
	ERR_FAIL_NULL(new_editor);
	if (editor_plugin_screen == new_editor) {
		return;