This is a good and fair question (although noting that the doses in the second study seem extremely large compared to supplement values). I think the solution is to test, test, and test on as many things as possible which is not being done at the moment. Most supplements will probably not have any notable effect, like L-theanine in my case, so a precautionary principle would lead one to discontinue use.

High doses of green tea extract is not the same as isolated L-theanine. You'd have to show research on the latter here.

The writing in that first paper is so poor that it's hard to take it too seriously, but it's a narrative review, not a study. The second link is a study on a few rats.