For a 10 hour stopover in Busan, I'd recommend checking out a few of the top attractions that are easy to visit independently. The Gamcheon Culture Village is really cool - it's a neighborhood built on steep hills with brightly colored houses, so it has great photo ops. You can easily spend a couple hours wandering around there. Haeundae Beach is also really nice, especially if it's a sunny day. You could grab some street food like tteokbokki or hotteok along the beach.
I found this great guide on things to see and do in Busan
https://gowithguide.com/blog/tourism-in-busan-statistics-2023-the-ultimate-guide-5543 It has information on transportation, popular neighborhoods, foods to try, and more.
Hope this gives you a few easy options to consider for your stop in Busan!