Something about this feels off context wise to the next pick, I feel Shouhou was saying Tenryuu was happier when the admiral was being praised

Well, it's just a the way of speech. She basically means "You look more happy while the admiral get praised than you getting them yourself don't you?". But as Japaneses just like cutting off their sentence and not repeat what is obvious, it's like this here. At least, that what I see through the Japaneses I know.