Probably pandoc protects whatever is inside $...$ or $$...$$. GitHub doesn't. I would be curious to know how pandoc handles the other failing cases.

There are many approaches to this problem. E.g., Jupyter notebooks implement one that has matured in the wild over a decade. There's this very flexible markdown-it plugin that implements anther https://github.com/goessner/markdown-it-texmath, and my version of it here https://github.com/sagemathinc/cocalc/blob/master/src/packag... which I rewrote in typescript with a focus on the same semantics as Jupyter has, but for CoCalc. I've also been working on using unifiedjs to provide more general latex for Markdown (not just formulas) here https://github.com/sagemathinc/cocalc/pull/5982

Parsing math in markdown is easier if you use a plugin to an existing markdown parser, rather than trying to do some hack outside of that (which is what Github probably does, and also what Jupyter does).