I searched online but I can't find the official reason why it is called a "Tea" Restaurant. Below is my guess and I hope I can explain it in more details :)Hello @theia7 thank you so much for your question! It is really thought-provoking :)
I guess it is because a Tea Restaurant is previously known as an "ice house"(冰室) - same meaning as a cafe, which mostly served western drinks (like milk tea or coffee) but not any formal meals.
As time went by, people started offering meals in ice house and so there was a change in its name into a "restaurant". To distinguish a Tea Restaurant from ordinary restaurant, they put "Tea" in front, showing this type of restaurant also offered western drinks.
Steem on!! 🤓