Unless the manga and lightnovel changed the setting a bit there is no exp boost.
The american ninja bath simply makes a person able to benefit more from training, the results of training show faster and more efficently, at a point the soldier will hit a cap, that being reaching their absolut peak of physical fitness.
This isekai have no levels, blessings or magic, everything abnormal/paranormal/magical is in the dungeons, that is the real reason every dungeon hit a limit with the explorers, being normal humans the monsters simply became too strong after a while, and is limited to dungeons, as the miasma in them makes this miracle possible.
If a item is enchanted with some special effect it will stop working outside the dungeon, or have a extremly limited effect that falls the further is from it.
I know some readers expect special individuals with special abilities, but up to where I read the WN (latest chapters) there was no such individual, "only" extremely strong soldiers.