Why is the hydrolysis of ATP to AMP more energetic than the hydrolysis of ATP to ADP?
Dr. Larry Moran (Professor Emeritus in the Department of Biochemistry at the University of Toronto) has posted an nice article about the Free Energy of ATP Hydrolysis. Accordingly, some important concepts in biochemistry may be widely misunderstood and/or not well described in most textbooks. One of them is the free energy of ATP hydrolysis:

The traditional standard Gibbs free energy changes do not apply in biochemical system because there are $\ce{Mg^2+}$ ions, ionic strength, and $\mathrm{pH}$ involve in the transformation. The traditional standard Gibbs free energy changes are at $\pu{25 ^\circ C}$ $(\pu{298 K})$ and $\mathrm{pH} \ 7$. For reactions like ATP hydrolysis, we want a new &quot;standard&quot; that includes free $\ce{Mg^2+}$ ion concentration of $\pu{10^{-3} M}$ and an ionic strength $(I)$ of $\pu{0.25 M}$ (Ref.1).
The transformed Gibbs energy (denoted as $G'$) is defined by the following Legendre transform of the Gibbs energy $G$:
$$G' = G - n'(\ce{H+})\mu(\ce{H+}) - n'(\ce{Mg^2+})\mu(\ce{Mg^2+}) \tag1$$
where $\mu(\ce{H+})$ and $\mu(\ce{Mg^2+})$ are the specified chemical potential of $\ce{H+}$ and  $\ce{Mg^2+}$ at equilibrium, respectively, and $n'(\ce{H+})$ and $n'(\ce{Mg^2+})$ are the total amount of these ions (free and bound) in the system. Accordingly, following are the calculated new values for specific reactions:
$$
\begin{array}{l|c}
\text{Biochemical reaction} &amp; \Delta G'_\text{hydrolysis} \ (\pu{kJ mol-1})  \\
\hline
\ce{ATP + H2O -&gt; ADP + P_$i$ + H+} &amp; -32  \\
\ce{ATP + H2O -&gt; AMP + PP_$i$ + H+} &amp; -45  \\
\ce{AMP + H2O -&gt; Adinosine + P_$i$ + H+} &amp; -13  \\
\ce{PP_$i$ + H2O -&gt; 2P_$i$} &amp; -29  \\
\hline
\end{array}
$$

References:

Robert A. Alberty, Robert N. Goldberg, “Standard thermodynamic formation properties for the adenosine 5'-triphosphate series,” Biochemistry 1992, 31(43), 10610–10615 (https://doi.org/10.1021/bi00158a025).