"Statistical significance" is a tricky and somewhat controversial issue regardless of the specific context of mediation analysis. Regardless of the general debate as to whether "statistical significance testing" is useful at all, I would be hesitant (or at least cautious) to interpret a "significant" indirect effect when the b path (or the a path) themselves are not "significant" and/or not substantial in size. That is, it does not make sense to me logically that there could be a "significant" indirect effect of X on Y when either the a or b paths are not statistically different from zero. When the b path is zero in the population, this means M does not cause variation in Y. In that case, there cannot be an indirect effect of X on Y via M.

That being said, this may be an issue of statistical power. You may have enough power to show that the indirect effect is "significantly different from zero" using the bootstrap confidence interval, while you do not have sufficient power to "detect" the b path alone as "significant." The stronger a path may drive the "significance" of the indirect effect. (Notice however, that the lower bound for your confidence interval for the indirect effect is also really close to zero.)

Hi Christian Geiser, thanks for taking the time to look through this and for your reply, it has been really helpful, thank you.

Hi Emma, Thank you for your question. While I wouldn't be clear-minded enough on this yet to contribute a helpful answer, I just wanted to say that I'm basically pondering on similar questions with my analyses. So, I'm always happy to link in/discuss/share if every of interest! Best wishes, Siwan