make4ht was not present in Tex Live 2013 and I used
mk4ht oolatex instead. I probably obtained a reasonable
result on a newer Tex Live (I don't remember the version
and I'm not sure whether I used make4ht or mk4ht)
on Debian Stretch (with problems with Russian characters
I didn't recognize at that time).
After upgrading to Debian Bullseye,
I haven't been able to obtain .docx as before.

Thank you, this configuration file worked and now I don't have
to move back and forth between different environments.

I attach the resultant test3-old.odt for your examination
using

mk4ht oolatex test3.tex

on Tex Live 2013.

(file #490)

Although this may be a problem involving libreoffice,
could you be kind enough to provide a hint?

[source]
\documentclass[12pt,a4paper]{article}

\usepackage[comma,colon]{natbib}
\def\cite{\citealt}
\setcitestyle{aysep={}}

\begin{document}

\citet{ale16baikalraptorphd}

\citep{ant20middleamur}

\begin{thebibliography}{}

\bibitem[{Alekseenko}(2016)]{ale16baikalraptorphd}
{Alekseenko}, M.~N. (2016) \textit{Ecological aspects of fall migration of
raptors in south Baikal migration corridor.} PhD Thesis, Bratsk State Univ.,
Bratsk (in Russian.)

\bibitem[{Antonov}(2020)]{ant20middleamur}
{Antonov}, A.~I. (2020) Expansion of new bird species in the {Middle Amur}
region at the end of the 20th century: the role of climatic changes. {\it
Rus. J. Ornithol.\,} 29: 4819-4827 (in Russian.)

\end{thebibliography}{}

\end{document}

After make4ht -f odt test3.tex, \citet and \citetp parts
have extra [ ] in .odt. When I converted it to .docx,
the citation keys disappeared. When I converted it to .pdf,
they were converted to "Error: Reference source not found".
It looks like some information may be missing in
the odt file.

What it wrong with my usage?

make4ht version is v0.3f

The same thing did not happen with mk4ht in Tex Live
in 2013.