The artist of the recent cherry blossom Madara and Hashirama official illustration tweeted an additional short explanation of the design motif meaning (for the new badge merch)! I enjoyed her explanation a lot so I translated it to English:
I'm delighted that the backing paper for these pin badges have been unified in design with the 霞文 (kasumi-mon or e-kasumi) pattern.
In this illustration, a design motif resembling the katakana character "エ" has been overlaid over the cherry blossoms.
This is a 吉祥文様 (kichi-jō monyō), which is a traditional auspicious symbol that represents continuity and longevity, and it reflects the feelings of the two characters at this point in the story.
















