Generalized studies are hard to come by because of the wide range of injuries. Studies usually focus on specifics. With youth sports, the issue is diagnoses, when to determine soreness VS injury. Kids, especially the high performing ones, tend to want to hide injuries.
A good rule of thumb is to determine soreness vs an injury. Soreness has a much shorter duration, generally 1-3 days. If pain lingers beyond 3 days, it's usually a good idea to rest and see your pediatrician, or if you have a sports ortho handy, see them. Soreness tends to cover larger areas of your body, pain tends to localize in joints and muscles. Think of a dead leg vs general leg muscle soreness.
There isn't a specific guidline for kids, they are so different. As they get older, >12, treatments are alwaysa good idea: massage, stretching, core, chiro, ice bath, massage guns, etc. Can get pricy to maintain an energetic and high performing athlete. Besides, they think they are bullet proof until they are not.