>And you are right that the following text is still shifted too close to the fancy logo.

Really? I don't see this trouble anymore with the "fancylogo" option and:

\documentclass{article}
\begin{document}
\noindent\LaTeX{} foo

\noindent\LaTeX foo

\noindent\LaTeX{}.

\noindent\LaTeX.
\end{document}

Well, I don't remember (8 years later ;) what I got at the moment, but, currently with:

<pre>
File List
article.cls 2019/12/20 v1.4l Standard LaTeX document class
size10.clo 2019/12/20 v1.4l Standard LaTeX file (size option)
tex4ht.sty
article.4ht
l3backend-dvips.def 2020-06-29 L3 backend support: dvips
l3backend-dvips.def 2020-06-29 L3 backend support: dvips
***********
</pre>
the "\LaTeX" logo is displayed just as "LaTeX":

<code>
<!--l. 14--><p class="noindent" >LaTeX
</code>

Maybe this explains the issue seems fixed. I wonder what we would get if the logo would be preserved in the HTML output.

Well, not that good: the entire "LaTeX" word is shifted to the right and a spurious space appears at its left.

Thanks to http://edward.oconnor.cx/2007/08/tex-poshlet a (working I hope) workaround would be:

\Css{.tex, .latex, .tex sub, .latex sub {
    font-size: 1em;
  }
}
\Css{.tex sub, .latex sub, .latex sup {
    text-transform: uppercase;
  }
}
\Css{.latex sub, .tex sub {
    vertical-align: -0.25em;
    margin-left: -0.1667em;
    margin-right: -0.125em;
  }
}
\Css{.latex sup {
    font-size: 0.85em;
    vertical-align: 0.15em;
    margin-left: -0.36em;
    margin-right: -0.15em;
  }
}

\def\TeX{\HCode{<span class="tex">}T\HCode{<sub>}e\HCode{</sub>}X\HCode{</span>}}
\def\LaTeX{\HCode{<span class="latex">}L\HCode{<sup>}a\HCode{</sup>}T\HCode{<sub>}e\HCode{</sub>}X\HCode{</span>}}

Hello,

there is an extra space in html output after some predefined TeX
commands, as pointed out by the following MCE (compile with htlatex
and with pdflatex in order to see the difference):

\documentclass{article}
\begin{document}
\noindent\LaTeX{} foo

\noindent\LaTeX foo
\end{document}

Best regards.