Right, what causal inference really gives you is a tool for specifying assumptions about a model of a data generating process and then estimating a parameter re

Right, what causal inference really gives you is a tool for specifying assumptions about a model of a data generating process and then estimating a parameter representing the effect size (and the uncertainty surrounding it), provided that your specified assumptions are approximately correct and your measurements are sufficiently accurate. It never directly answers a "why" or "how" type question. You provide the why/how and then use data to estimate "by how much?"