When I dine at a 'slightly more expensive' Chinese restaurant in Hong Kong or Guangzhou, Chinese tea is usually offered to diners. There are even eateries that has a tea menu for diners to select their tea. Tea is either charged per customer or by a serving of tea leaves. There are certain restaurants that offer tea brewing utensils like tea tray, electric kettle, fairness cup.....like brewing tea at home.....to make the tea drinking session more intricate during dining. I find the cost of tea at these establishments in my experience, not too expensive.
Pairing drinks with food is supposedly to be easy and pleasant. I felt that if the drinks do not make the dining experience unpleasant, the drinks are suitable. I had eaten at western eateries where I could select a glass (or 2 or 3) of wine to accompany my meal. Wine drinking is different from tea. Wine is to be sipped and swirled in the mouth before drinking. It is not appropriate if you find a food extremely spicy .... you reach out for your wine and gulp down the entire contents to 'extinguish' the spiciness. You could do that with Chinese tea. It would be different how a diner approach Chinese tea and wine during a meal. In Japan, I had warm sake to accompany my meal. It is surprising refreshing (and intoxicating). I recommend you try it.
To me, good wine or good Chinese tea should be appreciated on its own. Drinking them after dining would be a good idea. I appreciate the aroma and taste better when I drink them without any accompanying food.
I feel kinda hungry now.