South Korea has 3 festivals in this guide, spread across 2 cities. They run in June, July and August, and festival-day temperatures range from 28°C (82°F) to 30°C (86°F), with nights down to 19°C (66°F). That range is the reason there is no single "South Korea festival outfit". The answer changes by month and by site.
Every one of them run in real heat (28°C or more), where loose natural fabrics beat coverage and a brimmed hat does more than any garment. 2 carry a high rain risk, which makes waterproof footwear a requirement rather than a precaution.
The ground matters as much as the sky. You will find arena grounds and open field, which puts waterproof boots at the top of the list for most of these events. 1 of the 3 has camping on site, so outfits have to survive living in a bag on the ground for several days.
Stylistically the crowd here leans k-pop, y2k, streetwear and rave. Ultra Korea is the largest of them at around 100,000 people, and it sets the tone the smaller ones react to. None of that is a dress code. It is what you will see, which is worth knowing if you would rather blend in or deliberately not.