A marginnote in an equation is not typeset in a Hebrew document

Question

A description of the problem by way of a minimal working example

I saved the following LaTeX code in the file ~/Test.tex.

\documentclass{article}
\usepackage[hmarginratio=1:4]{geometry}
\usepackage[bidi=basic,hebrew,provide=*]{babel}
\usepackage{marginnote}
\makeatletter
\newif\if@RTL  \@RTLtrue
\makeatother
\begin{document}
\[
x + y = z\marginnote{Hello, world!}
\]
\end{document}

The code creates a document of class article, and adjusts the relative width of the article's left and right margins. It then establishes Hebrew as the document's main, and only language via the babel package. Then, after loading the marginnote package, it implements a hack suggested by Javier Bezos to resolve an issue arising when the marginnote package interacts with Hebrew documents managed by babel. Then, in the document's body, an equation, in which a margin note is embedded, is written in display mode.

Then I executed the following commands in the Terminal.

> cd ~
> lualatex Test
> lualatex Test

The compilation completed successfully, with no warning in ~/Test.log; in particular, no warning suggesting to rerun lualatex. As a consequence of the compilation, the file ~/Test.pdf was created. When opened in a PDF viewer the file displayed as follows. (I screenshot only the relevant part of the display.)

As can be seen, there's no margin note on the page.

Questions

1. Why wasn't the margin note printed out?
2. What can I do to make the margin note appear without giving up on the elements that make up the preamble: the geometry package with adjusted margins, the babel package with Hebrew as the main language, and Javier Bezos' hack. (Actually, the hack can be done away with, as long as it is replaced by another solution to this problem, but I'd prefer it if Bezos' elegant hack could be retained.)

Answer 1

Qustion 1

The margin note actually is printed out, but, because the margin note is typeset inside math mode, the direction of kerning (which the package marginnote heavily rely upon) is opposite to that outside of math mode, which makes the margin note flush outside the right margin of the page (due to wrong calculation of the package, that expected kerning to be done to the right).

You can observe that by moving your margin note more to the left

\documentclass{article}
\usepackage[hmarginratio=1:4]{geometry}
\usepackage[bidi=basic,hebrew,provide=*]{babel}
\usepackage{marginnote}
\makeatletter
\newif\if@RTL  \@RTLtrue
\makeatother
\begin{document}
    \[
    x + y = z\marginnote{Hello, world!}\cos (2\theta) = \cos^2 \theta - \sin^2 \theta
    \]
\end{document}

Question 2

You can exit math mode by entering restricted horizontal mode (via \hbox) and restore the direction of \pardir and \textdir (that has changed inside math mode)

\documentclass{article}
\usepackage[hmarginratio=1:4,showframe]{geometry}
\usepackage[bidi=basic,hebrew,provide=*]{babel}
\usepackage{marginnote}
\makeatletter
\newif\if@RTL  \@RTLtrue
\makeatother
\begin{document}
    \[
    x + y = z\hbox{\pardir TRT \textdir TRT\marginnote{Hello, world!}}
    \]
\end{document}

but it might be better to use \hboxR from luabidi, which does essentially the same, but is more robust

\documentclass{article}
\usepackage[hmarginratio=1:4,showframe]{geometry}
\usepackage[bidi=basic,hebrew,provide=*]{babel}
\usepackage{marginnote}
\usepackage{luabidi}
\makeatletter
\@RTLtrue % luabidi already defines this conditional
\makeatother
\begin{document}
    \[
    x + y = z\hboxR{\marginnote{Hello, world!}}
    \]
\end{document}