Centering itemize in Beamer

Question

I'm trying to (automatically) center an itemize in a Beamer presentation.

The problem is, that all solutions I've found either

• use varwidth with enumitem (which works a charm but not in beamer),
• use a table (which would cost me the exact overlay syntax from itemize/enumerate/description, which I'd prefer to keep, as the environment will be used by others) or
• manually size a minipage (or something similar).

So I started writing an environment that tries to calculate the width of an itemize to set a minipage to the correct width. The document below works as expected, what doesn’t work is nesting the lists.

So two questions:

• I don’t really know where to go from here. Can the problem be fixed (e.g. by changing the order of how stuff is calculated, as a minipage in the place of the nested list works)? Or do I need another approach? If the same syntax (i.e. \begin{ul}[<+-] and \item<...> with nesting) is possible with other methods that would also be fine, I'd just like the user-facing syntax to be familiar.
• I currently use \leftmargini in the width calculation, I don't really understand how I would detect in which “layer” I am and whether to apply \leftmarginii/\leftmarginiii.

\documentclass{beamer}
% adapted from https://tex.stackexchange.com/a/127014
\ExplSyntaxOn
\NewDocumentEnvironment{measureItemize}{+b}
{%
  % split the contents at \item
  \seq_set_split:Nnn \l_werner_itemize_input_seq {\item} {#1}
  % remove the first (empty) item
  \seq_pop_left:NN \l_werner_itemize_input_seq \l_tmpa_tl
  % measure each item
  \seq_map_inline:Nn \l_werner_itemize_input_seq {\measureitem{##1}}
}
{}
\seq_new:N \l_werner_itemize_input_seq
% adapted from https://tex.stackexchange.com/a/185707
\newlength{\xitemlenx}
\newlength{\xitemleny}
\newcommand{\measureitem}[1]{%
  \settowidth{\dimen0}{#1}%
  \ifdim\dimen0>\xitemlenx%
    \xitemlenx=\dimen0
  \fi
  \global\xitemleny\xitemlenx%
}
\NewDocumentEnvironment{ul}{o+b}
{%
    \begin{measureItemize}
        #2
    \end{measureItemize}
    \bigskip
    \begin{minipage}{\dim_min:nn {\linewidth} {\xitemleny+\labelsep+\itemindent+\leftmargini}}
        \begin{itemize}[#1]
            #2
        \end{itemize}
    \end{minipage}
    \bigskip
}{}
\ExplSyntaxOff
\begin{document}
\begin{frame}
    \centering
    \fbox{
    \begin{ul}[<+->]
        \item item 1
        \item item 2 is a bit longer
        \item item 3
        % \begin{ul}
        %     \item item 1
        %     \item item 2
        %     \item item 3
        % \end{ul}
    \end{ul}
    }
\end{frame}
\end{document}

Answer 1

Using a table does not mean you can't use overlays. You could for example adapt this answer by @CarLaTeX https://topanswers.xyz/tex?q=2000#a2242 :

\documentclass{beamer}
\makeatletter
\newcommand{\slideinframe}{\beamer@slideinframe}
\makeatother
\usepackage{tabularray}
\UseTblrLibrary{counter}
\UseTblrLibrary{varwidth}
\begin{document}
    \begin{frame}
  \centering
    \fbox{\begin{tblr}{colspec={l},
                cells={cmd=\onslide<\arabic{rownum}->,preto={{\usebeamercolor[fg]{itemize item}\usebeamertemplate{itemize item}~}}},
      }
            item 1 \
            item 2 \
        \end{tblr}}
    \end{frame}
\end{document}