Hi @elizevin,
As in LaTeX, when you defined \documentclass[12pt]{article}, you can increase font size, not setting it explicitly, but using the font size modifiers,\large{}, \Large{}, \huge{}, \Huge{}, for the LaTeX string to be displayed with a bigger fontsize than the default one, i.e. \normalsize{}.
Hence the only change, you have to perform in your code, is to set:
x_title=r'$\large{\rm{12+\log{Z_g}}}$', y_title=r'$\large{\rm{Merger \ rate \ [Gyr^{-1}]}}$'
or \Large{}, depending on your preferrence, and to remove the annotation updates for font size…
To use the same font family for the entire plot , i.e. for x_title, y_title, as well as subplot titles and subplot ticklabels, I suggest to set font_family='Open Sans' in your figc.layout.