What constitutes evidence when the links between exposure and outcome are indirect, delayed, or influenced by multiple interacting factors? And how can we strengthen our ability to interpret patterns

There are no rules for doing this; ignore anything that implies that there are as bad advice. In particular, ignore anything that implies that causation is observable under particular circumstances but not others. Your frustration is legitimate, in that causation is never observable and the more complicated a system gets the more ancillary hypotheses are needed before you can believe you are seeing evidence in support of a causal conclusion.

There are various things you can consider when reaching your causal conclusion. Obviously the basic quality of the evidence matters: Would a particular bit of evidence even support a causal claim if it were as good as it could be? Is there any serious recognition by those providing the evidence that there might be uncertainty due to errors in the methods? Are potential confounders chosen based on some real (stated) theory of the causal mechanism, or did the researchers just throw a bunch of covariates because they happened to have them? Do the authors seem to be choosing their model to best fit their data to get a result they prefer?

Once you can get past those hurdles (which in epidemiology pretty much always means trying to figure out what would have resulted had the authors done the right thing, because they didn't), you can start asking questions. Whatever the (or your) model of the causal process is, it will include some testable ancillary hypotheses, like "if this is real, we would expect a stronger signal when...." or "we would expect the association to disappear if...". There is no recipe for figuring those out for the general, and there may or may not be a history that suggests them to you for the particular case. You have to think scientifically.