In essence, it is a recycled version of an older post that was adapted to the specific example given in the question. The solution is based on animate's JS API, and on the beamer class' internal \ifbeamer@anotherslide.
All requested features have been addressed. Also, the current playing state (paused or playing, forwards or backwards) and the current frame rate of the animation are communicated between overlays. Successfully tested to work with Acrobat Reader and with Okular.
Use it as follows and note the way of how the animation is labelled, <label>_\thepage, and of how the label is used with the bracketing commands, \putBeforeAnim{<label>}/\putAfterAnim{<label>}. Also, mind the draft option in the alternative clause of \doifvisible.
\doifvisible{%
\putBeforeAnim{duck}%
\animategraphics[label=duck_\thepage,controls,loop]{1}{example-image-duck}{}{}%
\putAfterAnim{duck}%
}{
\phantom{\animategraphics[draft,controls,loop]{1}{example-image-duck}{}{}}%
}
Complete example. Just ignore the undefined references warning. (The warning is harmless and is because of placing \animategraphics in a \phantom box. To be fixed in the next version.)
\documentclass[12pt,aspectratio=1610]{beamer}
\usepackage{adjustbox}
\usepackage{animate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \putBeforeAnim{<label>}
% \animategraphics[label=<label>\thepage,...]{..}{..}{..}{..}
% or
% \begin{animateinline}[label=<label>\thepage,...]{..}
% ...
% \end{animateinline}
% \putAfterAnim{<label>}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand\putBeforeAnim[1]{%
\myPdfAnnot{1ex}{1ex}{0pt}{%
/Subtype/Widget/FT/Btn/Ff 65537/T (#1_a_\thepage)%
/AA <<%
/PC << % exec on page-close
/S/JavaScript /JS (
try{
var #1CurFrame =anim['#1_\thepage'].frameNum;
var #1CurSpeed =anim['#1_\thepage'].speed;
var #1PlayingFwd=anim['#1_\thepage'].isPlaying&& anim['#1_\thepage'].playsFwd;
var #1PlayingBwd=anim['#1_\thepage'].isPlaying&&(!anim['#1_\thepage'].playsFwd);
} catch(e){}
)
>>
>>%
}%
}
\newcommand\putAfterAnim[1]{%
\myPdfAnnot{1ex}{1ex}{0pt}{%
/Subtype/Widget/FT/Btn/Ff 65537/T (#1_b_\thepage)%
/AA <<%
/PO << % exec on page-open
/S/JavaScript /JS (
try{
anim['#1_\thepage'].frameNum=#1CurFrame;
anim['#1_\thepage'].speed=#1CurSpeed;
if(#1PlayingFwd){anim['#1_\thepage'].playFwd();}
if(#1PlayingBwd){anim['#1_\thepage'].playBwd();}
} catch(e){}
)
>>
>>
}%
}
\ExplSyntaxOn
\let\myPdfAnnot\pbs_pdfannot:nnnn
\ExplSyntaxOff
\makeatletter
\newcommand\doifvisible[2]{\ifbeamer@anotherslide #2\else #1\fi}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\section{Section 1}
\begin{frame}[t]{Frame Title}
\begin{columns}[t]
\begin{column}{0.5\textwidth}
\pause
\adjincludegraphics[width=\linewidth,valign=t,center]{example-image-a}
\pause
[
Kim=Jong+Un
]
\end{column}
\begin{column}{0.5\textwidth}
\pause
\begin{adjustbox}{width=\linewidth,valign=t,center}
\doifvisible{%
\putBeforeAnim{duck}%
\animategraphics[label=duck_\thepage,controls,loop]{1}{example-image-duck}{}{}%
\putAfterAnim{duck}%
}{%
\phantom{\animategraphics[draft,controls,loop]{1}{example-image-duck}{}{}}%
}
\end{adjustbox}
\pause
\begin{itemize}
\item Kim Jong Un\pause
\item Peace Be Upon Him\pause
\end{itemize}
\begin{center}
The end of the world!
\end{center}
\end{column}
\end{columns}
\end{frame}
\end{document}