Embedding currently selected Sensitivity Label in Word document

Hi,

I'm looking for a way to embed the currently selected Sensitivity Label in the content of a Word document by using Quick Parts. Partly because I want it to show when printed. I would not like to resort to using the functions that apply watermark or text in header/footer that is configured in the label configurations unless there is no way to achieve what I need.

My understanding is that the Sensitivity Label should be stored as a document property. But I can't seem to find it among the properties.

Any help in this matter would be greatly appreciated.