Superimpose Matlab figure to Mathematica figure, not vectorized

A PDF vectorized plot is generated from a MatLab figure. Import this Matlab PDF figure to Mathematica and superimpose it onto a Mathematica figure. Finally in Mathematica, export this Mathematica and Matlab figure as a vectorized PDF plot. It turns out the MatLab part of the figure is not a vectorized plot. No such issue when there's no Matlab involved. I'm using Mathematica 11 and 14.3 in Windows. How to resolve it? Example with my code for Matlab and Mathematica:

[X,Y] = meshgrid(-5:.5:5);
Z = Y.*sin(X) - X.*cos(Y);
s = surf(X,Y,Z,'FaceAlpha',0.5)
exportgraphics(gcf,'vectorfig.pdf','ContentType','vector')

Show[Plot[x, {x, 0, 1}], 
    Epilog -> {Inset[Import["vectorfig.pdf"][[1]], {0.5, 0.5}, Center, {Automatic, 0.4} ]}]