Short Answer Questions
As you can see in your post, if the Moodle TeX filter is working properly, then equations will get rendered wherever you put them in places like the question text.
However, if the student types an equation as the answer to a short-answer question, that will not be rendered.
So, basically, what are you trying to do?
The response the student types into a shortanswer question is not processed in any way. Some people write shortanswer questions about programming, or other technical areas, where special characters are important, and should not be messed around with.
If you want an question type that accepts TeX source ans input, and displays rendered TeX on review, then that would have to be a different question type.
One question type that does that, plus a whole lot more, is STACK: https://moodle.org/plugins/view.php?plugin=qtype_stack - but that is massive overkill for what you want.