Currently only rich text content controls and check box content controls are available through the Word API https://learn.microsoft.com/en-us/javascript/api/word/word.contentcontrol?view=word-js-prev...
We also need this, especially the date picker. Our Word Add-in gets the complete Word document (xml), makes changes to is and then we place the complete document back. If there are locked content controls in the the document this does not work. Then we first unlock to content controls, then replace the adjusted xml and then we lock the content controls again.
This means that we need to unlock all the content controls. At this moment it is not possible to unlock the date picker so our add-in does not work with documents with a locked date picker.