The styles are there! The text is not in the normal style. Surprising behavior in Word 2010 pasting into a new document that has a base of Body Text, using "Use Destination Styles!" Exeption, in Word 2010, pasting into a document in which the styles had not been used preserved the numbering. I just checked and that is how it is behaving in Word 2010, as well. The Body Text Level 3 style is a custom style. The pasted text is all in the Normal style. The original text was in Heading 1, Heading 2, Heading 3, Body Text Level 3, and Body Text paragraph styles. Here is a screenshot from a recipient document that contains both a screenshot from the source text as it is copied and the pasted text using "Keep Source Formatting." There is no method of pasting this text, with numbered styles, that carries the style formatting into the new document. "Keep Source Formatting" copies character-level formatting as direct formatting in the Normal style. I am telling you that the documentation is wrong. I do not disagree that what you are showing is the documentation. This is how it has worked until one of the recent updates. Keep Source Formatting is supposed to copy all of the formatting in the selected text to the destination document when pasted.
Graphical elements are discarded, and tables are converted to a series of paragraphs. The text takes on the style characteristics of the paragraph where it is pasted and takes on any direct formatting or character style properties of text that immediately precedes the cursor when the text is pasted. Keep Text Only (T) This option discards all formatting and nontext elements such as pictures or tables. When selected, choose options from the Picture Format tab. The text can't be changed, but you can treat it like any other picture or image and use effects, borders, or rotation. Picture (U) This option is only available on Microsoft 365 Subscription. Converts text into an image and pastes that. The text also takes on any direct formatting or character style properties of text that immediately precedes the cursor when the text is pasted. The text takes on the style characteristics of the paragraph where it is pasted. Merge Formatting (M) This option discards most formatting that was applied directly to the copied text, but it retains formatting that is considered emphasis, such as bold and italic, when it is applied to only a portion of the selection.
Any style definition that is associated with the copied text is copied to the destination document. Keep Source Formatting (K) This option retains formatting that was applied to the copied text.
That is wrong and not what the documentation says per Microsoft.