moderncardthemes VS MathJax

Simply go to the GitHub repository and scroll down, should have left a note for people not familiar with GitHub, sorry.

MathJax - Mathematical Notations expressed using Tex or MathML

Developer tools point to MathJax https://www.mathjax.org/. If you disable javascript you can see some LaTex.

It is something we could add, but it is not planned in the near future. We also have requests for adding math notation (like https://www.mathjax.org/), and that could be a more general solution.

I don't know what Obsidian is, but if it's requiring old TeX math mode toggles (the double dollar sign), then it might not actually be using LaTeX underneath. Many tools that provide LaTeX-style syntax for equations are actually using something like MathJaX, BlahTex, or some custom system by which to translate LaTeX-like syntax into their own equation rendering. This often means you only get a pre-defined subset of what's possible with LaTeX (and the results are never quite faithful to how LaTeX would typeset them).

This will depend heavily on where you're asking the question, e.g. stackexchange has built in mathjax to render it. I'm going to assume you're intending to ask here (because that would make sense), in which case check out the bottom of the sidebar.

From the screenshot, Obsidian looks like a typical Markdown editor that supports some LaTeX math syntax, probably rendered with something like Mathjax. On the other hand, Xournalapp seems to actually use LaTeX, even allowing you to use LaTeX packages like graphicx, tikz, etc.