First, realize that the LaTeXStrings package does not do any LaTeX rendering — it’s simply a way of entering strings of LaTeX math without lots of escapes. The actually rendering is done by the plotting backend, which in your example is Matplotlib (via PyPlot.jl). Matplotlib, in turn, uses its own LaTeX math renderer. Some other Plots.jl backends use mathjax, some use MathTeXEngine.jl, and yet other plotting backends don’t support LaTeX math at all.
Typically, the most you can hope for that these backends render standard LaTeX math macros. The \mathfrak macro, however, is not standard LaTeX — it is provided by the amsfonts package. Similarly, \boldsymbol is provided by amsbsy (included by amsmath).
(If you want, it is possible to get Matplotlib to use a full LaTeX renderer, assuming you have it installed, in which case you can use arbitrary LaTeX packages if you configure things correctly.)