I am not convinced that most tea has sugar already added. Teas I have looked at contain "100%" tea.
Looking at Carbohydrate content on their website (made without milk, which is how I drink it)
Twinings Assam 0g Carbohydrate
Twinings Earl Grey 0g Carbohydrate
Twinings Strong English Breakfsat 0g Carbohydrate
Their Herbal teas have nutritional information on the packet - Carbohydrate
Pure Peppermint 0g, Lemon and Ginger 0g, Pure Camomile 0g
It is harder to find the nutritional information for Taylors of Harrogate, but the ingredients for example their Yorkshire Tea are listed as "Black Tea" If they were adding sugar then I think this would have to be listed on the ingredients.
Tetley give the ingedients as "Black Tea" and say on their website that there is 0.3g of carbohydrate per 100g. (0g sugar)
Christmas Tea will have other ingredients and I cannot find carbohydrate content of that.
I think that some websites list the nutritional information assuming that tea is made with milk, and if so, it is the milk that is providing the carbohydrate/sugar, not the tea itself. It is possible that some teas may add sugar, but I haven't found any and I am happy that the teas I drink do not.