Even though it is uncommon usage, QToolBar can appear in any widget other than QMainWindow.
This usage is explicitly documented in QToolBar documentation:

A toolbar is typically created by calling QMainWindow::addToolBar(const QString &title), but it can also be added as the first widget in a QVBoxLayout, for example.

However, QToolBar does not exist in the widget list in left dock of Designer. It can be added through context menu when using MainWindow as template.

I have tried to add a QWidget and change it to QToolBar by editing the XML file directly for test with non-MainWindow template file. The modified file is recognized by Designer without any problem, so I guess this kind of usage is just overlooked.