You can do something like this:

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

\usepackage[comma,colon]{natbib}
\newcommand\possiblebreak{\hspace{0pt}}

\begin{document}

\begin{thebibliography}{}

\bibitem[{Gulf News}(2021)]{gul21OHB}
{Gulf News} (2021) {Video: A rare migratory bird rescued by Dubai resident
(2021 May 20).}
Downloaded from https://gulfnews.com/\possiblebreak uae/\possiblebreak environment/\possiblebreak video-a-rare-migratory-bird-rescued-by-dubai-resident-1.79307000.

\end{thebibliography}

\end{document}
%%%%%%%%%%%%%%%%%

And then redefine the \possiblebreak in the .cfg file:

%%%%%%%%%%
\Preamble{xhtml}
\renewcommand\possiblebreak{\nobreak}
\begin{document}
\EndPreamble
%%%%%%%%%%

It seems that the Breakurl package inserts some PostScript code in the DVI mode. This causes TeX4ht error. It should be fixed with the attached usepackage.4ht and breakurl-hooks.4ht files.

Regarding the \hspace trick, you could also define a custom command for this purpose, and redefine it to do nothing with TeX4ht. But in general, I think that \url is better. It is weird that it doesn't break with platex. Unfortunatelly I am not familiar with this engine.

(file #505, file #506, file #507)

I tried with test10.tex and obtained different results
between teX4ht (test10.odt) and platex (test10.pdf).
The long URL line is not broken by platex.
I wanted to specify where to break (such as after &)
by using \hspace{0pt}. This worked as desired in platex,
but not in teX4ht.

If there is a good tip to produce similarly broken
long URLs by teX4ht and platex from the same .tex source,
I would be happy to know it.

(file #500, file #501, file #502)

Unnecessary spaces are inserted at \hspace{0pt}.
(platex-compiled test9.pdf is also attached).

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

\usepackage[comma,colon]{natbib}

\begin{document}

\begin{thebibliography}{}

\bibitem[{Gulf News}(2021)]{gul21OHB}
{Gulf News} (2021) {Video: A rare migratory bird rescued by Dubai resident
(2021 May 20).}
Downloaded from https://gulfnews.com/\hspace{0pt}uae/\hspace{0pt}environment/\hspace{0pt}video-a-rare-migratory-bird-rescued-by-dubai-resident-1.79307000.

\end{thebibliography}

\end{document}