Actually, there is a way to do this without too much manual intervention -- although it would be easiest to do this after all the pictures and their captions have been inserted.
When you click the built-in Insert Caption button, click the Numbering button, and check the "Include chapter number" box, the caption it inserts looks like this when the field codes are expanded by pressing Alt+F9:
Figure { STYLEREF 1 \s }.{ SEQ Figure \* ARABIC \s 1 }
The STYLEREF field inserts the number of the most recent Heading 1 paragraph, and the SEQ field inserts the next number in the Figure sequence (and restarts that sequence after each Heading 1 because of the \s 1 switch).
To make this arrangement work for figures under Heading 2 paragraphs, just change the two instances of the number 1 to the number 2:
Figure { STYLEREF 2 \s }.{ SEQ Figure \* ARABIC \s 2 }
Do that in the first caption that appears under a Heading 2, and then copy the fields and paste them into the rest of the captions that occur under any Heading 2. Finally, press Ctrl+A and then F9 to update all the fields, and then update the table of figures
separately.
Warning: After you've changed all those fields in the captions, if you then use the Insert Caption button to insert another caption, Word will undo all your work! If you need to add another caption at that point, do it by copying and pasting an existing
caption.