How can I thicken tea?
You could try using arrowroot. This is a widely available alternative to cornstarch - it is used in cookery because it doesn't turn liquids cloudy like cornstarch does. In your case, it might work better as it also has a more neutral flavour.

Substitute 2 tbsps of arrowroot for 1 tbsp cornstarch, and make a slurry with cool water as you would cornstarch. One issue is that overheating can break down the arrowroot, preventing it from thickening, so you are probably better off adding it to the tea after removing it from the heat.