Ooh, I love your idea of a cat cafe! I haven’t heard of anyone doing that yet, and it would be a great way to roll the tea room into it. I personally like the idea of a study as well. I recently redid one of my side rooms to be a sunroom/study for myself. Not a traditional office space, but more of a relaxing spot I would actually love to work in IRL.
Note the kitchenette space and kettle boiling, to feed my constant need for tea
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Another completely different idea could a be a games room/lounge. A place where you might hang out with friends, watch some TV, place some foosball, etc...