biblatex-chem's chem-biochem still uses some pre-3.3 code. See Biblatex 3.3 name formatting. In particular you need to replace \ifblank with \ifdefvoid.
\renewbibmacro*{name:family-given}[4]{%
\ifuseprefix
{\usebibmacro{name:delim}{#3#1}%
\usebibmacro{name:hook}{#3#1}%
\ifdefvoid{#3}{}
{\mkbibnameprefix{#3\isdot}%
\ifprefchar{}{\addhighpenspace}}%
\mkbibnamefamily{#1\isdot}%
\ifdefvoid{#2}{}
{\addcomma\addlowpenspace
\mkbibnamegiven{#2}\isdot}%
\ifdefvoid{#4}{}
{\addlowpenspace
\mkbibnamesuffix{#4}\isdot}}
{\usebibmacro{name:delim}{#1}%
\usebibmacro{name:hook}{#1}%
\mkbibnamefamily{#1}\isdot
\ifboolexpe{%
test {\ifdefvoid{#2}}
and
test {\ifdefvoid{#3}}}
{}
{\addcomma}%
\ifdefvoid{#2}{}
{\addlowpenspace
\mkbibnamegiven{#2}\isdot}%
\ifdefvoid{#3}{}
{\addlowpenspace
\mkbibnameprefix{#3}\isdot}%
\ifdefvoid{#4}{}
{\addlowpenspace
\mkbibnamesuffix{#4}\isdot}}%
}
The definition in chem-biochem.bbx using the old macros does not quite work with the new name format and causes a spurious space in certain situations. That's what you are seeing as an incorrect indentation.
With the fix your MWE from chem-biochem options not working becomes
\documentclass{article}
\usepackage[style=chem-biochem, biblabel=brackets]{biblatex}
\addbibresource{biblatex-examples.bib}
\makeatletter
\renewcommand*{\bibleftbracket}{\blx@postpunct[}
\renewcommand*{\bibrightbracket}{\blx@postpunct]\midsentence}
\makeatother
\DeclareFieldFormat{labelnumber}{#1}
\renewbibmacro*{name:family-given}[4]{%
\ifuseprefix
{\usebibmacro{name:delim}{#3#1}%
\usebibmacro{name:hook}{#3#1}%
\ifdefvoid{#3}{}
{\mkbibnameprefix{#3\isdot}%
\ifprefchar{}{\addhighpenspace}}%
\mkbibnamefamily{#1\isdot}%
\ifdefvoid{#2}{}
{\addcomma\addlowpenspace
\mkbibnamegiven{#2}\isdot}%
\ifdefvoid{#4}{}
{\addlowpenspace
\mkbibnamesuffix{#4}\isdot}}
{\usebibmacro{name:delim}{#1}%
\usebibmacro{name:hook}{#1}%
\mkbibnamefamily{#1}\isdot
\ifboolexpe{%
test {\ifdefvoid{#2}}
and
test {\ifdefvoid{#3}}}
{}
{\addcomma}%
\ifdefvoid{#2}{}
{\addlowpenspace
\mkbibnamegiven{#2}\isdot}%
\ifdefvoid{#3}{}
{\addlowpenspace
\mkbibnameprefix{#3}\isdot}%
\ifdefvoid{#4}{}
{\addlowpenspace
\mkbibnamesuffix{#4}\isdot}}%
}
\begin{document}
\cite{sigfridsson}
\printbibliography
\end{document}
