Instead of using the footmisc package, you could adapt this answer https://tex.stackexchange.com/a/169775/36296 . The size of the footnote box can be calculated from the text width + the right margin (1cm) - the width of the footnote mark (1.8em) - the space right of the page number (approximately 1em, but a bit smaller in reality as the page numbers use a small font, fine tune this value if you like).
\documentclass{beamer}
%\usepackage[hang,ragged]{footmisc}
\usepackage[backend=biber, maxnames=2, style=lncs]{biblatex}
\addbibresource{biblatex-examples.bib}
% custom citations (only author, title, year, DOI / arxiv):
\DeclareCiteCommand{\footcite}[\mkbibfootnote]
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\printnames[given-family]{author}:%
\setunit{\addspace}%
\printfield{title}%
\nobreak\setunit{\addspace}% discourage break here
\printfield{year}%
\iffieldundef{doi}
{\iffieldundef{eprint}
{} % no DOI or eprint, don't add the penalty
{\penalty-300 \setunit{\addspace}%
\printfield{eprint}}}
{\penalty-300 \setunit{\addspace}%
\printfield{doi}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\makeatletter
\renewcommand<>\beamer@framefootnotetext[1]{%
\global\setbox\beamer@footins\vbox{%
\hsize\framewidth
\textwidth\hsize
\columnwidth\hsize
\unvbox\beamer@footins
\reset@font\footnotesize
@parboxrestore
\protected@edef@currentlabel
{\csname p@footnote\endcsname@thefnmark}%
\color@begingroup
\uncover#2{@makefntext{%
\rule\z@\footnotesep\ignorespaces\parbox[t]{\dimexpr\textwidth+1cm-1.8em-1em}{#1@finalstrut\strutbox}\vskip1sp}}%
\color@endgroup}%
}
\makeatother
\setbeamertemplate{navigation symbols}{}
\setbeamertemplate{footline}[frame number]{}
\usepackage{lipsum}
\setbeamertemplate{footnote}
{
\parindent 1em\noindent%
\raggedright
\hbox to 1.8em{\insertfootnotemark}\insertfootnotetext\par%
}
\begin{document}
\begin{frame}
Hello World!\footcite{baez/article}
\lipsum[1-1]
\end{frame}
\end{document}

If you would just like to keep the date on the same line, you could remove the \raggedright from the footnote template. IMHO this will look nicer than having the date stick out into the margin.
\documentclass{beamer}
%\usepackage[hang,ragged]{footmisc}
\usepackage[backend=biber, maxnames=2, style=lncs]{biblatex}
\addbibresource{biblatex-examples.bib}
% custom citations (only author, title, year, DOI / arxiv):
\DeclareCiteCommand{\footcite}[\mkbibfootnote]
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\printnames[given-family]{author}:%
\setunit{\addspace}%
\printfield{title}%
\nobreak\setunit{\addspace}% discourage break here
\printfield{year}%
\iffieldundef{doi}
{\iffieldundef{eprint}
{} % no DOI or eprint, don't add the penalty
{\penalty-300 \setunit{\addspace}%
\printfield{eprint}}}
{\penalty-300 \setunit{\addspace}%
\printfield{doi}}}
{\multicitedelim}
{\usebibmacro{postnote}}
\makeatletter
\renewcommand<>\beamer@framefootnotetext[1]{%
\global\setbox\beamer@footins\vbox{%
\hsize\framewidth
\textwidth\hsize
\columnwidth\hsize
\unvbox\beamer@footins
\reset@font\footnotesize
@parboxrestore
\protected@edef@currentlabel
{\csname p@footnote\endcsname@thefnmark}%
\color@begingroup
\uncover#2{@makefntext{%
\rule\z@\footnotesep\ignorespaces\parbox[t]{\dimexpr\textwidth-1.8em}{#1@finalstrut\strutbox}\vskip1sp}}%
\color@endgroup}%
}
\makeatother
\setbeamertemplate{navigation symbols}{}
\setbeamertemplate{footline}[frame number]{}
\usepackage{lipsum}
\setbeamertemplate{footnote}
{
\parindent 1em\noindent%
% \raggedright
\hbox to 1.8em{\insertfootnotemark}\insertfootnotetext\par%
}
\begin{document}
\begin{frame}
Hello World!\footcite{baez/article}
\lipsum[1-1]
\end{frame}
\end{document}

biblatex-examples.bibis a bib file which is included in all commonly used tex distributions for this purpose. No need to include it. Also the code as shown in the question seems to work just fine on overleaf. – samcarter_is_at_topanswers.xyz Nov 02 '23 at 16:41