Using bm with eulervm gives inconsistent ‘<’ and ‘>’ characters

There is an inconsistency in the shape of < and > in the zeurm10 and zeurb10 fonts used for the symbols with eulervm active:

\documentclass{article}

\usepackage{amsmath}
\usepackage[euler-digits,euler-hat-accent]{eulervm}
\usepackage{bm}

\begin{document}

\begin{tabular}{@{}ll@{}}
bm: & $1 + 1 < 3$; $\bm{1 + 1 < 3}$ \\
mathbold: & $1 + 1 < 3$; $\mathbold{1 + 1 < 3}$
\end{tabular}

{\usefont{U}{zeur}{m}{n}\symbol{"3C}}

{\usefont{U}{zeur}{b}{n}\symbol{"3C}}

\end{document}

With \mathbold, which is a math alphabet selection, only letters and numbers become bold, but not other symbols.

You can work around the inconsistency by using Computer Modern for the < and > symbols.

\documentclass{article}

\usepackage{amsmath}
\usepackage[euler-digits,euler-hat-accent]{eulervm}
\usepackage{bm}

\DeclareSymbolFont{cmletters}{OML}{cmm}{m}{it}
\SetSymbolFont{cmletters}{bold}{OML}{cmm}{b}{it}
\DeclareMathSymbol{<}{\mathrel}{cmletters}{"3C}
\DeclareMathSymbol{>}{\mathrel}{cmletters}{"3E}

\begin{document}

\begin{tabular}{@{}ll@{}}
bm: & $1 + 1 < 3$; $\bm{1 + 1 < 3}$ \\
mathbold: & $1 + 1 < 3$; $\mathbold{1 + 1 < 3}$
\end{tabular}

\end{document}

\mathbold is math alphabet command (like \mathbf, \mathit etc) so it has no effect on < . \bm though does affect < and you get the character that the package sets up for \boldmath, If you add

\boldmath

 $ 1 + 1 < 3\showlists$

You will see that \bm is selecting (in normal math) the fonts used in \boldname.

In this case that is

....\U/zeur/b/n/10 <

But as you show the bold font's < is a rather different shape to the medium weight font

So this appears to be a font issue.