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This conditional independence is implied. Fixing the mediator at $m$ removes the directed edge $M\to Y$ in the relevant counterfactual graph. Conditioning on $A$ blocks $M\leftarrow A\leftrightarrow Y(m)$, while conditioning on $X$ blocks $M\leftarrow X\to Y(m)$. Every remaining path is blocked by the m-separation criterion, so

This conditional independence is implied. In the graph for $M(a)$, the incoming causal value of $A$ has been fixed, so the path $A\to M$ no longer transmits association to $M(a)$. The only possible route through $Y$ contains a collider, and conditioning on $X$ blocks the common-cause path through $X$. Hence m-separation gives