I'm glad you were able to get a solution.
In the screenshot you posted the leftmost image appears to be Firefox and not Safari. FWIW Firefox and Chrome do render differently even for me here.
But now looking at the inner html code and your first set of screenshots, I can see that the primary problem is that you are using local font names. I'm guessing you have the fonts actually installed. Safari 12+ no longer support using fonts installed on the system, so it isn't really a metrics problem but it is that the font is different.