From Causal Inference In Statistics, A Primer by Judea Pearl, I learnt that for linear SCMs (Structural Causal Model), the arrow strengths can be related to the appropriate linear regression coefficients. For example, in SCM -
$Y:=bX+cZ+U_3$, where $U_1,U_2,U_3$ are assumed to be independent of each other,
with causal graph -
the OLS (ordinary least squares) linear regression coefficient of $X$ when $Y$ is regressed on $X$ and $Z$, gives the coefficient $b$ in the SCM, i.e., the strength of the arrow $X \rightarrow Y$. The interpretation of this arrow's strength is that if $X$ is increased (via intervention) by 1 unit, $Y$ is supposed to increase by $b$ units.
In contrast to this interpretation, in the user guide for dowhy library, the interpretation is given in terms of KL-divergence and increment of variance; absence of the arrow $X \rightarrow Y$ increases the variance of $Y$ by certain units.
What is the significance/intuition behind this second form of interpretation and how does it relate to the first type (which is quite intuitive)?
Note: I am okay with references being provided to standard sources, in case I am lacking some major fundamental background. An explanation here itself, even if filled with mathematical notations, is even more preferable.