Why does $\mathcal L$ render as $\mathscr L$?
What packages get loaded in the preamble? Where can I find the preamble?
Can I add my own packages? What's with \mathcal being replaced by \mathscr?
MacBook
If you are referring to the built-in equation editor, and not Mathtype, then it has to do with a C++ compiled [La]TeX/MathML translator (blahtex) that transforms a restricted set of [La]TeX syntax into the embedded MathML equation. There is no underlying TeX implementation, and even if you had MacTeX 2019 installed, it would be ignored. No \usepackage statements are allowed.
You can read more about the [La]TeX equation support, including what syntax is accepted by blahtex here. Coincidentally, the syntax \mathscr L is not supported by \mathcal L or \mathcal{L} is supported.
You do not need the '$' delimiters for your equation in the equation editor because it is not the [La}TeX engine that is listening.