Vanishing math font styles in unicode-math due to a mess of mathtools, mathtt and using math fonts with ranges

It's a misfeature, but a workaround is to load again the main math font for the \mathscr range; you also have to declare anew the main math font.

\documentclass{article}
\usepackage{mathtools}
\usepackage{
    fontspec,
    unicode-math,
}

\setmathfont{Latin Modern Math}
\setmathfont{XITS Math}[
  range = \mathcal,
]
\setmathfont{Latin Modern Math}[
  range = \mathscr
]

\begin{document}

$A$
$\symtt{L}$
$\mathcal{L}$

\end{document}

Note that the correct call for a typewriter type variable is \symtt, or \mathtt would load the text monospaced font.

This is the pdffonts report:

BRCTEL+LatinModernMath-Regular-Identity-H CID Type 0C       yes yes yes      5  0
HSKWQU+XITSMath-Identity-H           CID Type 0C       yes yes yes      7  0