So, this is an instinct thing from how I’ve seen each used, slightly supported by jisho’s example sentences, but I think あと is less a time construct than an event construct… if that makes sense.
Jisho’s example sentence for あと (後) is:
雨天の後には晴天が来る
“After rain comes fair weather.”
So, the rain is the event that occurs, fair weather comes after.
Whereas the example for 過ぎ is:
10時過ぎには電話をしないで下さい。
“Don’t call me up after 10 o’clock.”
It indicates a time, explicitly.
I don’t know that you can’t use one or the other interchangeably, for sure, but other instances I have seen, seem to follow that general pattern. あと is for after an event, 過ぎ is for after a moment in time.
Somebody may correct that thought if it’s wrong, but it’s my gut instinct.
2nd Edit: Just moticed the furigana from Jisho copy and paste inserted itself into the srntence, and I didn’t delete them. Cleaned that up!
Editing to give another example of あと being used for an event, I don’t know if you are reading それでも歩は寄せてくる, but in Chapter 3, there is this panel:
Where she is saying, “After we have two more members gather, we can be a club.”
I knew I had seen it somewhere else recently. Heh.