Nice description of differences here: What is the difference between MathJax and QuickLaTeX? – Pressbooks Guide. Short answer is that the QuickLaTeX output will be images with alt text containint the LaTeX expression used to generate the image. It’s about as accessible as an image of a LaTeX expression can be, but it’s still an image with alt text that may not be easy to understand for an unsighted visitor.
The iMathAS math system (software that runs MyOpenMath and Lumen Learning OHM) has begun using MathJax version 3.2. It’s the first major software system I have seen that has made the jump.
It’s a rewrite a MathJax and not a minor upgrade, but one of the big changes I see as a user is that the speech extension is integrated more completely into core. I know we talked about this briefly in 2020, but now that speech engine rules that you mentioned have been brought into MathJax Core with the rewrite. MathJax is now able to produce subtitles without a screen reader with math player being used as a middle man to interpret the MathML.