Notification only occurs once per day even if you level up skills more than once. So a notification is not guaranteed. Let's just remove the mention of that entirely.
Each skill level adds +1 [[Axes|Axe]] [[Skills#Proficiency|proficiency]]. Although you will not receive a notification that you have leveled up in Foraging Skill until after you go to sleep for the day, your skills menu will immediately show the level up as a red bar in Foraging Skill. The effects of leveling up are immediate.
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Each skill level adds +1 [[Axes|Axe]] [[Skills#Proficiency|proficiency]]. The effects of leveling up occur immediately after leveling up.