### 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
Dictionary state;
	state["main_tab"] = _get_current_main_editor();
	state["scene_tree_offset"] = SceneTreeDock::get_singleton()->get_tree_editor()->get_scene_tree()->get_vscroll_bar()->get_value();
	state["property_edit_offset"] = InspectorDock::get_inspector_singleton()->get_scroll_offset();
	state["node_filter"] = SceneTreeDock::get_singleton()->get_filter();
	return state;
}
void EditorNode::_set_main_scene_state(Dictionary p_state, Node *p_for_scene) {
	if (get_edited_scene() != p_for_scene && p_for_scene != nullptr) {
		return; 
	}
	changing_scene = false;
	int current_tab = -1;
	for (int i = 0; i < editor_table.size(); i++) {
		if (editor_plugin_screen == editor_table[i]) {
			current_tab = i;
			break;
		}
	}
	if (p_state.has("editor_index")) {
		int index = p_state["editor_index"];
		if (current_tab < 2) { 
			if (index < 2 || !get_edited_scene()) {
				editor_select(index);
			}
		}