It is not a “different “ methodology, it is unreliable. Self reporting from participants is fraught with expectation bias. As far as number of participants, we are not told how many. And I note that the supplement melatonin is taken by some of the participants. That is illegal in this country. And above all, we are not told about medication that the participants were taking, or whether any change of medication took place during the study.
I don’t disagree that there is a connection between gut and brain, but that has been shown to be related to the gut biome - the bacteria in the gut - rather than specific foods or supplements.
There is probably a study that could be done to analyse the effect of food and supplements, but this isn’t it. It’s methodologically too shabby.