there are several things conspiring to make your example not work, compared to this version which does work

\documentclass{article}

\usepackage{unicode-math}
\setmathfont{Stix Two Math}

\begin{document}

\Umathcodenum`ħ=`ħ


hbar: $\hbar$



hbar unicode (U+0127): $ħ$



hslash: $\hslash$



hslash unicode (U+210F): $ℏ$



\end{document}

The Latin modern math font doesn't have U+0127, Stix does, but it does not work by default as U+0127 doesn't have a mathcode nor does the unicode-math-table.tex define \hbar, just \hslash.

the default math codes are based on the Uniocde data file MathClass-15.txt which is in texlive as
texmf-dist/tex/generic/unicode-data/MathClass-15.txt
and that only lists U+210F

One other issue that the engine default is math fam 1 but unicode-math sets everything in fam 0 and fam1 stays as the 7 bit computer math italic, so if you take a random character that does not get a specific math code from the data file

\Umathcharnumdef\zzz=\Umathcodenum"100DB
\show\zzz

\showthe\textfont1

you see:

> \zzz=\Umathchar"7"01"0100DB.
l.18 \show\zzz
            
? 
> \OML/cmm/m/it/10 .
l.20 \showthe\textfont1

so as with hbar even if the open type fonts have the character the default in math is to take the character from computer modern math.

unicode-math could put the main font in slot 1 as well as slot 0 but that may have compatibility issues.

Thanks for your reply. I'll admit I'm not an expert with all this, in particular the fonts.

The Latin modern math font doesn't have U+0127

By default, latex include \hbar with a horizontal bar, and amssymb define the \hslash macro. Are these both not from the Latin modern font? E.g. if I do not use unicode-math and instead add amssymb I obtain:

unicode-math itself makes \hbar equivalent to \hslash, which is an other issue as well...

the default math codes are based on the Uniocde data file MathClass-15.txt which is in texlive as
texmf-dist/tex/generic/unicode-data/MathClass-15.txt
and that only lists U+210F

I suppose \hbar U+0127 is considered text then. Assuming that this doesn't change, is the command you used, that is

\Umathcodenum`ħ=`ħ

the "proper" way to add input characters to unicode-math?

It probably isn't the proper way , but it works, without having to look up the character number,making the character come from the font in fam 0 (and act like a fixed symbol, not changing for \mathbf etc)

If you wanted to define \hslash you could use the form used in unicode-math-table.tex

\UnicodeMathSymbol{"0210F}{\hslash                   }{\mathalpha}{/hslash - variant planck's over 2pi}%

(note I don't have write access here, just an interested observer....)

For reference, \hbar is included as a math symbol here: https://www.w3.org/Math/characters/unicode.xml

unicode.xml is my file:-) actually the latest (Uniocde 13) version is https://w3c.github.io/xml-entities/unicode.xml

210F has

      <character id="U0210F" dec="8463" mode="math" type="alphabetic">
         <unicodedata category="Ll" combclass="0" bidi="L" decomp="&lt;font&gt; 0127" mirror="N" unicode1="PLANCK CONSTANT OVER 2 PI" mathclass="N"/>
         <afii>EF68</afii>
         <latex>\hslash </latex>
         <mathlatex set="unicode-math">\hslash</mathlatex>

0127 has

      <character id="U00127" dec="295" mode="math" type="alphabetic">
         <unicodedata category="Ll" combclass="0" bidi="L" mirror="N" unicode1="LATIN SMALL LETTER H BAR" upper="0126" title="0126"/>
         <afii>E2EB</afii>
         <latex>\Elzxh </latex>

note the lack of a mathclass entry in <unicodedata (because it is not in MathClass-15.txt) and lack of <mathlatex> element (as it is not in unicode-math-table.tex)

For classic tex \hbar is not a character in the font it is a small horizontal bar sone negative space then an h.

the problem is that Unicode has a specific slot for this (U+0127) so in xetex of luatex the character is just passes straight through as data like h but then if the font does not have that character you get no output and a Missing Character warning in the log file. You could set things up to over-print a bar and an h in unicode-math as well, but then (without more complicated tests) fonts like Stix that do have the character would "lose" the character and also get the constructed version