If you want to test out some examples from your website to see how they'd look in KaTeX vs. browser MathML rendering, I made a tool for that here: https://mk12.github.io/web-math-demo/
Nice tool! Seems "New Computer Modern" font is the Native MathML rendering that looks closest like standard LaTeX rendering, I guess cause LaTeX uses Computer Modern by default. But I notice extra space around the parenthesis, which annoys me because LaTeX math allows you to be so precise about how wide your spaces (e.g. \, \: \; \!). Is there a way to get the spaces around the parenthesis to be just as wide as standard LaTeX math? And the ^ hat above f(x) isn't nicely above just the top part of the f.
Assuming you’re seeing the same issue as me: I find the parenthesis spacing is messed up whenever there are unnecessary \left and \right, as there are in some of the samples, which leads to an extra <mrow> in the MathML. If you only use those when they really need to stretch, then it looks much better.