Another fantastic question that merits clarification. A major challenge I sense here again, as has happened in a prior thread, is the different terminologies / notations used between fields. @Sander belongs to the rare breed that can seamlessly connect them but they otherwise remain a great source of misunderstanding.
Fully cognizant that it can be an oversimplification, it helps in this case to adopt Pearl’s demarcation between statistical (associational) concepts such as collapsibility, odds ratios, hazard ratios, regression etc and causal concepts such as confounding, randomization, instrumental variables etc. Our review focused on causal concepts whereas all your questions refer to statistical concepts. Thus, when we say “neutral” we do not refer to statistical effect modification (e.g., a multiplicative interaction in a regression model) but a variable that does not confound (in the causal sense), mediate or serve as a collider for the exposure-outcome relationship of interest. This is described both in our aforementioned review and other references offered both there and in this thread.
The difference in terminologies between statisticians and causal inference methodologists applies to the term “bias” as well, and you are very correct that I should have clarified this. @AndersHuitfeldt excellently elaborated on this distinction in this thread. Your comment on bias follows the statistical definition and the related bias-variance trade-off. I am working on a draft paper where we do, for example, connect the bias-variance trade-off with causal concepts, consistent with the notion that the demarcation between “statistical” and “causal” is far from perfect even though in our particular thread here it helps us maintain focus.