First thing, if you put something in your body, it has some effect, even if that effect is small. "No effect" results just rule out effects above different effect sizes (both positive and negative) with high probability, and there's no point talking about "a link" like it's some discrete thing (you sort of jump back and forth between getting this one right and wrong).

Second, different studies will rule out different effect sizes with 95% confidence - or to put it another way, at a given effect size, different studies will have different p-values, and so your probability exercise was pretty pointless because you didn't compare the studies' opinions about any particular effect size, just "whatever was 95%."

Third, I'd bet a nickel the effect sizes ruled out at 95% in all of these studies are well below the point where it would become concerning (like, say, the effect of the parents being a year older). That is, these studies all likely rule out a concerning effect size with probability much better than 95%.