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You got the tranlsation and intended meaning correct on your own, so well done there. ~ようとする is actually a grammar point on its own, so that might help you fill in the gaps you may have in your understanding!
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I would say it is a state of being, because, where it’s a verb directly preceding a noun, it is modifying the 女の子 to say they are in the state of 見学してる.
One way to look at らしい is that it is often used in situations where the speaker is passing on information from a source besides themselves. This source could be a textbook, another person, or anything like that. I would also say it kinda modifies this entire sentence and not just the 痛い. It basically modifies everything before it, in the instances I’ve run into it.
Either way, while you can say, “Seems like~” for らしい, another English interpretation could be, “I have heard~” or “Apparently~”
With that in mind, a more natural translation:
“Apparently (or I have heard that), menstruation is a pain in the stomach.”
(Which is like, a super simplification of what menstruation is, but they are middle school boys, so they wouldn’t really have all the info, unless sex-ed is actually thorough in explanations over there, which would honestly surprise me.)
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