The bark produces a balsam named Storax, it was used as cough medicine, and to heal wounds and skin infections, IRL it is harvested by scraping the outer bark and after a few days a thick amber resin that is the Storax appears. In game we could harvest the resin by haversting the bark and when it grows back you also get an option to harvest the sap. to turn into the balsam in game it should be boiling cauldron + sweetgum sap + clay jar = Storax Balsam, it could be used to treat bee stings or scrapes over time.
The fruitpods produce shikimic acid wich is necessary to make anti flu medicine, so if we ever get the flu in game, we already got the means to fight it. This should be something you use in an alchemist table to create a medicine.
Well i dont think we'll ever have diarrhea or dysentery in the game (i can't thank Jorb enough for that), but we have swamp fever, it will heal over time, and the sweetgum bark can be turned into tea that will treat all these problems, so what i had in mind was, boiling cauldron + 3 or more sweetgum barks + clayjar = Sweetgum bark tea that makes the swamp fever heals faster.
Also sweetgum trees could get a special bark type in the game

The sap of a sweetgum tree was used and still is used as a natural chewing gum, the sweetgum sap the Storax is a natural chewing gum that could be equiped in the mouth slot, i searched for the effects of chewing gum, it increase alertness and attention up to 10%, basically increasing your focus, and it also lowers stress levels, so maybe it could give a + to perception, since focus is perception (this is optional BS). maybe we could even get an animation of the character mouth moving.
Sorry for any typing errors