Say that I appended to document an inline picture contained in a file called figure_file_name as follows:
add_picture(figure_file_name)
Then, say that I am subsequently creating a caption as follows:

p = document.paragraphs[-1]
p.alignment = WD_ALIGN_PARAGRAPH.CENTER
caption = document.add_paragraph("Text of the caption goes here", style='Caption')
caption.alignment = WD_ALIGN_PARAGRAPH.CENTER

How do I then make this paragraph, which has the Caption style indeed, actually behave like a caption, i.e., move with the figure (and possibly refer to it with a Fig. 1 marking), as if it had been created in the MS Word GUI?

If I am not missing anything, the API currently does not allow for it. It would be a nice feature to have however. Thank you.