Can a tufte-latex file output tufte-css HTML?

It is possible to configure TeX4ht to produce output expected by Tufte HTML. At the moment, I have working verbatim, notes, bibliography, sections, maketitle and figures.

Here is a sample document:

documentclass[]{tufte-book}
usepackage{kantlipsum}
usepackage{url}
usepackage{graphicx}
begin{document}
title{Sample Document}
author{Michal Hoftich}
maketitle
tableofcontents
section{Introduction}

This is an example of Tufte LaTeX document converted to Tufte HTML using TeX4htfootnote{url{https://tug.org/tex4ht/}}.
It shows various commands provided by Tufte classes. Most of the text are just random words 
provided by the Kantlipsumfootnote{url{https://ctan.org/pkg/kantlipsum?lang=en}} package, so please don't 
try to find a message in that.

begin{marginfigure}
  includegraphics[width=textwidth]{example-image.png}
  caption{Example margin figure}
end{marginfigure}

section{First section}

Here is some math: (a^2+b^2=c^2)

[e^{ipi}+1=0]

kant[1]

subsection{Hello, subsection}


begin{figure}[tbt]
  caption{Example figure}
  includegraphics[width=textwidth]{exports-imports.png}
end{figure}

kant[2]

% begin{margintable}
%   begin{tabular}{l l}
%     hello & world\
%     second & line
%   end{tabular}
%   caption{Margin table}
% end{margintable}

begin{figure*}[tbt]
  includegraphics[width=textwidth]{napoleons-march.png}
  caption{Full width figure}
end{figure*}
begin{verbatim}
Hello verbatim 
Some special characters: {|} % "
end{verbatim}

newthought{We can try thought} allcaps{uppercase} textit{příliš žluťoučký kůň} kant[3]

I am also interested in footnotesfootnote{Hello, this is a footnote}. kant[4]

Another paragraph, try sidenote this timesidenote{This is a sidenote}. And also marginnotemarginnote{Hello, this is a marginnote}.

I want to try citationscite{Tufte2001,Tufte1990,Tufte1997,Tufte2006}.

begin{fullwidth}
  This paragraphs is in full size kant[5]
 end{fullwidth}



bibliography{sample-handout}
bibliographystyle{plainnat}


end{document}

I've used this .bib file to test the bibliography support.

The support is now just in the form of a .cfg file:

Preamble{xhtml}
% add tufte.css to your document
Configure{AddCss}{tufte.css}

% helper macro to close the current paragraph
defendparagraph{ifvmodeIgnoreParfiEndP}

% insert <article> element to the document body
Configure{@BODY}{endparagraphHCode{<article>}}
Configure{@/BODY}{endparagraphHCode{</article>}}

% Tufte LaTeX makes section and subsection to behave like section* and subsection*
% so we need to configure like<section level>
% These configurations insert <section> elements and print titles in apropriate header elements
Configure{likesection}
{endparagraphHCode{<section>}}{endparagraphHCode{</section>}}
{HCode{<h2>}}{HCode{</h2>}parShowPar}

Configure{likesubsection}
{endparagraphHCode{<section>}}{endparagraphHCode{</section>}}
{HCode{<h3>}}{HCode{</h3>}parShowPar}

% we must redefine TOC to print starred sectioning commands
% TableOfContents is provided by TeX4ht
renewcommandtableofcontents{endparagraphHCode{<h2>Contents</h2>Hnewline}TableOfContents[likesection,likesubsection]}

% custom maketitle
makeatletter
renewcommand{maketitle}{%
  begingroup%
    endparagraphHCode{<h1>}@titleHCode{</h1>}%
    HCode{<p class="subtitle">}@authorHCode{</p>}%
    HCode{<p class="subtitle">}@dateHCode{</p>}%
  endgroup
}

% make images resize automatically
Configure{Gin-dim}{}
Css{img {
    max-width: 100%;
    height: auto;
}}

% fix for commands redefined by soul
@ifpackageloaded{soul}{%
renewcommand{allcaps}[1]{MakeTextUppercase{#1}}%
renewcommand{smallcaps}[1]{{scshapeMakeTextLowercase{#1}}}%
renewcommand{textsc}[1]{textcaps{#1}}%
}{}

% footnotes and sidenotes

longdef@tufte@sidenote[#1][#2]#3{%
  stepcounter@mpfn%
bgroup% make font changes local
  HCode{<label for="sitenote-thempfn" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sidenote-thempfn" class="margin-toggle" />}%
  HCode{<span class="sidenote">}#3HCode{</span>}%
egroup%
}
renewcommandmarginnote[2][0pt]{%
  stepcounter@mpfn%
bgroup% make font changes local
  HCode{<label for="sitenote-thempfn" class="margin-toggle"></label><input type="checkbox" id="sidenote-thempfn" class="margin-toggle" />}%
  HCode{<span class="marginnote">}#2HCode{</span>}%
egroup%
}

% environments

ConfigureEnv{verbatim}{endparagraphHCode{<pre><code>}NoFonts}{EndNoFontsendparagraphHCode{</code></pre>}}{}{}
ConfigureEnv{fullwidth}{endparagraphHCode{<div class="fullwidth">}%
ConfigureList{list}{}{}{}{}% fullwidth uses list environment internally, we don't need this
parShowParindent% require insertion of paragraph
}
{endparagraphHCode{</div>}}{}{}

% floats

NewConfigure{marginfloat}{2}

% redefine internal margin float environment in order to prevent use of minipage and other undersirable environments
renewenvironment{@tufte@margin@float}[2][-1.2ex]%
{FloatBarrier% process all floats before this point so the figure/table numbers stay in order.
begingroup%
lettextwidthmarginparwidth% includegraphics[width=textwidth]{...} should work
def@captype{#2}%
par%
% redefine paragraph
Configure{HtmlPar}{EndPcsname a:marginfloatendcsname}{EndPcsname a:marginfloatendcsname}{csname b:marginfloatendcsname}{csname b:marginfloatendcsname}%
}
{endgroup}

Configure{marginfloat}{HCode{<p><span class="marginnote">}
% we must handle caption inside marginnote
Configure{caption}{HCode{<span class="figure">}}{:space}{}{HCode{</span>}}
}{HCode{</span></p>}}{}{}

% display marginnote caption on a separate line
Css{.marginnote .figure{display:block;}}

renewenvironment{@tufte@float}[3][htbp]%
{@float{#2}[#1]}{end@float}

% caption should produce margin note by default
Configure{caption}{HCode{<span class="marginnote">}}{:space}{}{HCode{</span>}}

% figure* should produce full width image
% we need to make few adjustments
ConfigureEnv{figure*}{
Configure{float}{}{endparagraphHCode{<figure class="fullwidth">}}{endparagraphHCode{</figure>}csname parendcsnameShowPar}
Configure{caption}{endparagraphHCode{<span class="figure">}}{:space}{}{HCode{</span>}}
}{}{}{}

ConfigureEnv{margintable}{endparagraphHCode{<div class="margintable">}Configure{caption}{}{:space}{}{}}{endparagraphHCode{</div>}}{}{}

% fix for display math length
Css{div.math-display, div.par-math-display {width: 55%}}

makeatother

begin{document}
EndPreamble

Save it as myconfig.cfg. The document can be compiled using:

pdflatex sample.tex
bibtex sample
make4ht -m draft -c myconfig.cfg sample.tex "mathml,mathjax"

This is the rendered document: