I have personally observed something similar with black tea but I am not sure if's just the theanine + EGCGs or something else.

A while back, I noticed that 'chai' helps me focus and relax (improved mood, less anxiety, etc.) at the same time. It's made of milk, black tea, cardamom, cinnamon, and negligible/no sugar (personal preference).

I prefer coffee in terms of taste, but of all the things I have tried, this has been the best for me. Black tea alone doesn't have the same effect on me, nor does green tea, or coffee with or without milk/cream/sugar.

So I wonder if it's the combination that matter and not theanine alone.