Yes, I travelled between ICN and NRT with a 14 year old recently and we filled up a large cabin bag with food from South Korea.

No fruit and, as we carried only hand luggage, nothing liquid (Kimchi is specifically banned as a hand luggage item on Asiana so you can’t even buy it at the airport). Food is generally sold in much bigger packs than in Japan, this might present more of a challenge than you’re expecting.

Since my kid had the chance to compare the food haul from S Korea and what was available in Japan, when we stayed in S Korea again for the return trip, the only candy re-chosen for own consumption as well as gifts for friends was the Orion range of gummy+jelly candies in 67g packs. Favourite was the kiwi version but all these gummy flavours were deemed a hit. This page shows the grape version.
https://mykmarket.com/products/461054

You’ll see racks upon racks of “langue de chat” cookies at ICN airport in an array of flavours, don’t bother. There is no comparison between these and their counterparts sold in NRT/HND.