Strange behaviour in importing symbols from stix package

Question

I was importing symbols from the stix package (brackets in particular) following the directives given here on tex.stackexchange when something really strange happend, which I presume has to deal with the font encoding LS2. In particular I imported the sequent symbols, succesfully

\DeclareFontEncoding{LS2}{}{}
\DeclareFontSubstitution{LS2}{stix}{m}{n}
\DeclareSymbolFont{largesymbols}{LS2}{stixex}{m}{n}
    \DeclareMathDelimiter{\lBrace}{\mathopen}{largesymbols}{"E8}{largesymbols}{"0E}
    \DeclareMathDelimiter{\rBrace}{\mathclose}{largesymbols}{"E9}{largesymbols}{"0F}
    \DeclareMathDelimiter{\lBrack}{\mathopen}{largesymbols}{"E0}{largesymbols}{"06}
    \DeclareMathDelimiter{\rBrack}{\mathclose}{largesymbols}{"E1}{largesymbols}{"07}
\DeclareSymbolFont{largesymbolsstix}{LS2}{stixex}{m}{n}
    \DeclareMathDelimiter{\lbrbrak}{\mathopen}{largesymbolsstix}{"EE}{largesymbolsstix}{"14}
    \DeclareMathDelimiter{\rbrbrak}{\mathclose}{largesymbolsstix}{"EF}{largesymbolsstix}{"15}

which are exactly what I want. But the problem is that all the basic latex symbols seem to be gone; a simple code, with a sum, and some partial derivatives, for example, gives this bad outcome

where the right symbol now are only the two imported brace \lBrace and \rBrace. Now, if I comment the part in which I declare the symbols

    \DeclareFontEncoding{LS2}{}{}
    \DeclareFontSubstitution{LS2}{stix}{m}{n}
%   \DeclareSymbolFont{largesymbols}{LS2}{stixex}{m}{n}
%       \DeclareMathDelimiter{\lBrace}{\mathopen}{largesymbols}{"E8}{largesymbols}{"0E}
%       \DeclareMathDelimiter{\rBrace}{\mathclose}{largesymbols}{"E9}{largesymbols}{"0F}
%       \DeclareMathDelimiter{\lBrack}{\mathopen}{largesymbols}{"E0}{largesymbols}{"06}
%       \DeclareMathDelimiter{\rBrack}{\mathclose}{largesymbols}{"E1}{largesymbols}{"07}
%   \DeclareSymbolFont{largesymbolsstix}{LS2}{stixex}{m}{n}
%       \DeclareMathDelimiter{\lbrbrak}{\mathopen}{largesymbolsstix}{"EE}{largesymbolsstix}{"14}
%       \DeclareMathDelimiter{\rbrbrak}{\mathclose}{largesymbolsstix}{"EF}{largesymbolsstix}{"15}

everything is back to normality, but with no more the two brackets desired from the stix package (I replaced manually the two braces, otherwise it would have not compiled):

Does anyone know how to fix it? Thanks!

EDIT:

I found that the true problem comes with the \DeclareSymbolFont{largesymbols}{LS2}{stixex}{m}{n}, as there is already a default setup for the class largesymbols, which is \DeclareSymbolFont{largesymbols}{OMX}{cmex}{m}{n}. But the problem still stands still, as the one exclude the other. How can I use those symbols along with the standard latex ones?

Answer 1

Here, I replaced your largesymbols with largesymbolsstix and gave it a spin. Is this sufficient?

(As noted in the OP's edit, largesymbols is already employed by LaTeX)

\documentclass{amsart}

\makeatletter
\DeclareFontEncoding{LS2}{}{\@noaccents}
\makeatother
\DeclareFontSubstitution{LS2}{stix}{m}{n}

\DeclareSymbolFont{largesymbolsstix}{LS2}{stixex}{m}{n}

\DeclareMathDelimiter{\lBrace}{\mathopen}{largesymbolsstix}{"E8}{largesymbolsstix}{"0E}
\DeclareMathDelimiter{\rBrace}{\mathclose}{largesymbolsstix}{"E9}{largesymbolsstix}{"0F}
\DeclareMathDelimiter{\lBrack}{\mathopen}{largesymbolsstix}{"E0}{largesymbolsstix}{"06}
\DeclareMathDelimiter{\rBrack}{\mathclose}{largesymbolsstix}{"E1}{largesymbolsstix}{"07}

\DeclareMathDelimiter{\lbrbrak}{\mathopen}{largesymbolsstix}{"EE}{largesymbolsstix}{"14}
\DeclareMathDelimiter{\rbrbrak}{\mathclose}{largesymbolsstix}{"EF}{largesymbolsstix}{"15}
\newcommand{\newbrak}[2]{\genfrac{\lbrbrak}{\rbrbrak}{0pt}{}{#1}{#2}}
\begin{document}
\[
\newbrak{k}{m} = 
\lBrace A, B \rBrace = \sum_{k=1}^3
  \biggl\lBrack \frac{\partial A}{\partial q_k}\biggr\rBrack
\]
\end{document}