What makes it confusing is when the discussion compares the same framing versus the same distance to subject.
If you need more reach, and the camera stays in the same place, adding a TC will
the depth of field. Only if you move the camera backward so that you have the same image as without the TC, will the depth of field
remain the same
So, for wildlife where you merely need more focal length and can't get closer, you get
LESS depth of field with the TC. For a portrait, if you already have a good composition, its very unlikely that you would add a TC and then move backwards, so that is not a common usage of a TC.
Here is a image taken at a close distance with my 70-200mm at f/4 and a 1.4X TC. The brown wall in the background was about a foot away and very much out of focus. The bird was about 10 ft away and is cropped.
You can do this by adding a TC and getting closer to the subject, which decreases the depth of field.
With my 1D MK III, the depth of field with TC at 10 ft is 0.09 ft, If I did not move, just removed the TC, it would be increased to 0.13 ft.