What is the simplest, most canonical way to change the background color of quoted text?

A simple code based on framed and quoting which can break across pages:

\documentclass{article}
\usepackage[x11names]{xcolor}
\usepackage{framed}
\usepackage{quoting}

 \colorlet{shadecolor}{LavenderBlush2}
\usepackage{lipsum}
\newenvironment{shadedquotation}
 {\begin{shaded*}
  \quoting[leftmargin=0pt, vskip=0pt]
 }
 {\endquoting
 \end{shaded*}
}

\begin{document}

\lipsum*[1-4]
\begin{shadedquotation}
\lipsum*[5-6]
\end{shadedquotation}
\lipsum*[7-10]

\end{document} 

Color support needs xcolor (or just color).

\documentclass{article}
\usepackage{xcolor}

\usepackage{lipsum} % for mock text

\newsavebox{\coloredquotationbox}
\newenvironment{coloredquotation}
 {%
  \begin{trivlist}
  \begin{lrbox}{\coloredquotationbox}
  \begin{minipage}{\dimexpr\linewidth-2\fboxsep}
 }
 {%
  \end{minipage}
  \end{lrbox}
  \item\relax
  \parbox{\linewidth}{
    \begingroup
    \color[RGB]{224,215,188}%
    \hrule
    \color[RGB]{249,245,233}%
    \hrule
    \color[RGB]{224,215,188}%
    \hrule
    \endgroup
    \colorbox[RGB]{249,245,233}{\usebox{\coloredquotationbox}}\par\nointerlineskip
    \begingroup
    \color[RGB]{224,215,188}%
    \hrule
    \color[RGB]{249,245,233}%
    \hrule
    \color[RGB]{224,215,188}%
    \hrule
    \endgroup
  }
  \end{trivlist}
 }

\begin{document}

\lipsum*[3]
\begin{coloredquotation}
\lipsum*[4]
\end{coloredquotation}
\lipsum*[5]

\end{document}

An example with tcolorbox (is not almost canonical?) was missing.

\documentclass{article}
\usepackage[most]{tcolorbox}
\usepackage{lipsum}

\definecolor{linequote}{RGB}{224,215,188}
\definecolor{backquote}{RGB}{249,245,233}

\newtcolorbox{myquote}{%
    enhanced, breakable, 
    size=fbox,
    frame hidden, boxrule=0pt,
    sharp corners,
    colback=backquote,
    borderline horizontal={.5pt}{0pt}{linequote},
    borderline horizontal={.5pt}{1pt}{linequote}
}

%% Important!!
%% Use ! before "O{}" with xparse 2018-05-12 
%% See: https://tex.stackexchange.com/q/434928/1952
\NewTCBListing{mycode}{ !O{} }{%
    enhanced, breakable, 
    size=fbox,
    frame hidden, boxrule=0pt,
    sharp corners,
    colback=gray!30,
    listing only, 
    listing options={%
        style=tcblatex,
        keywordstyle=\color{brown!70!black},
        texcsstyle=*\color{brown!70!black}
    },
    #1}

\listfiles
\begin{document}
\lipsum[1]

\begin{myquote}
\lipsum[2]
\end{myquote}

\begin{mycode}
\documentclass{article}
\begin{document}
    Hello
\end{document}
\end{mycode}

\end{document}

Update A minimal default version with an optional parameter to change anything.

\documentclass{article}
\usepackage[most]{tcolorbox}
\usepackage{lipsum}

\definecolor{linequote}{RGB}{224,215,188}
\definecolor{backquote}{RGB}{249,245,233}

\newtcolorbox{myquote}[1][]{%
    enhanced, breakable, 
    size=minimal,
    frame hidden, boxrule=0pt,
    sharp corners,
    colback=backquote,
    #1
}


\begin{document}
\lipsum[2]

\begin{myquote}
\lipsum[2]
\end{myquote}

\begin{myquote}[colback=red!30, size=small]
\lipsum[2]
\end{myquote}

\end{document}