Why exactly does high pressure (72 bar) nitrous oxide's pseudocritical¹ temperature drop so far when oxygen is added to make 50%v/v mixture? (Entonox)
Dissolution(solvation) is solvation of solute molecules by molecules of solvents. This decreases chemical potential $\mu={\left(\frac{\partial G}{\partial n}\right)}_{T,p}$ of the solute, comparing it (often hypothetically ) to the chemical potential of the solute at the same concentration in gaseous phase.
Different solvents cause different chemical potential drop, leading to different solubility. As dissolution equilibrium means the equal solute chemical potentials in the solid phase and the solution.
Chemical  potential and fugacity

It [fugacity] is equal to the pressure of an ideal gas which has the same temperature and molar Gibbs free energy[=chemical potential] as the real gas.

are linked by relation $\mu=\mu_0 + RT \ln{\frac{f}{f_0}} \tag{1}$
Molecules in gaseous phase move independently on each other, unless there is a strong chemical affinity, what is not this case. Pointing effect does not depend(*) on the used gas, as there is no molecular wrapping in gas.
Pointing effect does not directly affect chemical potential of vapor. But  pressure affects the chemical potential of liquid instead, leading to higher saturated vapor pressure at the same temperature. The vapor pressure therefore increases to balance chemical potentials of the  substance in both phases.
For liquids near their critical conditions, like for the case of nitrous oxide with or without oxygen, there are big changes of state variables like molar volume or density with small change of conditions like pressure and temperature. This leads to relatively big change of saturated vapor pressure with the change of pressure of the system.
Note that for the liquid at its critical temperature $T_\mathrm{c}$ and near its critical pressure $p_\mathrm{c}$, $$\lim_{p \to p_c}{\ \left(\frac {\partial V}{\partial p}\right)}_{T }= -\infty \tag{2} $$
to get a picture what these changes are like.
As we know from the thermodynamics, for stable composition and zero non-volume work:
$$\mathrm{d}G=-S \cdot \mathrm{d}T + V. \mathrm{d}p  \tag{3}$$
Therefore $${\ \left(\frac {\partial G}{\partial p}\right)}_{T }=V \tag{4}$$
$${\ \left(\frac {\partial \mu_\mathrm{liq}}{\partial p}\right)}_{T }=V_\mathrm{m, liq} \tag{5}$$
If we assume ideal vapor behavior, we can consider $p_\mathrm{vap} = f_\mathrm{vap}$ and
$$RT \cdot {\left(\frac{ d \ln{p_\mathrm{vap}}}{\mathrm{d}p}\right)}_T =  V_\mathrm{m, liq} \tag{6}$$
$$RT \cdot \ln {\frac{p_\mathrm{vap}}{p^{\circ}_\mathrm{vap}}} =  V_\mathrm{m, liq} \cdot (p - p^{\circ}_\mathrm{vap}) \tag{7}$$
$$ p_\mathrm{vap}  =  p^{\circ}_\mathrm{vap} \cdot \exp {\left(\frac {V_\mathrm{m, liq}}{RT} \cdot (p - p^{\circ}_\mathrm{vap})\right)} \tag{7}$$
(7) is a simplified saturated vapor pressure dependency rather for &quot;normal&quot; liquids with $T_\mathrm{c} \gg T$, when the liquid compressibility can be neglected. Otherwise, $V_\mathrm{m,liq}=f(p)$ would have to be included to the integration, as the liquid molar volume and compressibility start steeply grow toward the critical point. E.g. water vapour and liquid densities converge to about $\rho = \pu{0.21 g/cm}$ at the water critical point.
For illustration, we can take water at the boiling point with
$V_\mathrm{m} = M/\rho = (\pu{18.02 g/mol})/(\pu{0.9584 g/cm3})=\pu{18.8 cm3/mol}$, $T=\pu{373 K}$ a $p^{\circ}_\mathrm{vap}=\pu{e5 Pa}$. It can be seen the pressure effect can be neglected for small and medium pressure.
$\begin{array}{cc}\small \\
\text{pressure [MPa]} &amp; \text{H2O vapor pressure [kPa]} \\
0.1 &amp; 100.0 \\
0.2 &amp; 100.1 \\
0.5 &amp; 100.2 \\
1.0 &amp; 100.5 \\
2.0 &amp; 101.2 \\
5.0 &amp; 103 \\
10 &amp; 106 \\
20 &amp; 113 \\
50 &amp; 135 \\
100 &amp; 183 \\
\end{array}$

(*) Special cases are systems with significant chemical interactions, including gas solubility in liquid. E.g. well soluble gases cause additional effect of the opposite sign than the Pointing effect. They decrease the saturated vapour pressure by decreasing solvent molar fraction and eventually its chemical potential in both phases by chemical interaction. E.g. $\ce{NH3(g + aq),H2O(l + g)}$.