I always thought that 坊 in 朝寝坊する was a bit weird. At least in Chinese, 坊 means "small factory". Thus I assumed it was a pun about "went to work at the morning sleeping factory" though it seems a bit far-fetched. How come it is not just 朝寝する or even 朝寝る?
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坊 in Japanese is fairly uncommon on its own, but it means something like 'kid' or 'boy' most of the time (originally it was 'monk', and it's shifted a bit semantically). 寝坊 is a somewhat playful term for someone who has trouble getting up in the morning, and as a する verb means 'sleep late' or 'oversleep'. 朝寝坊する is basically the same thing.
坊's modern Chinese meaning is probably the result of it being used as the simplification of an unrelated character, but I could be wrong.
(This is an answer based on observation and experience but if you do some research I think you will find some substance:)
The use of 坊 literally means boy or son but rather like -man in English, it can sometimes be used to mean person, of either sex: