냐 싶다

you might well ask ~, but

-냐 is the blunt question ending and 싶다 after it reports the question as a passing thought rather than a real one. Five of these six lines run on into a 'but' — 싶지만, 싶긴 해, 싶으실 수 있는데 — because the speaker raises the doubt in order to knock it down: 먹방 하는데 웬 헬스장이냐 싶으실 수 있는데 (you may wonder what a gym is doing in a mukbang, but...). The question is usually rhetorical, meaning the opposite of what it asks.

Register: conversational; used to anticipate the audience