Update
With a current version of biblatex, you can use bibstring sets. See https://tex.stackexchange.com/a/644877/35864.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber, style=authoryear]{biblatex}
\DefineBibliographyExtras{british}{%
\DeclareBibstringSet{latin}{andothers,ibidem}%
\DeclareBibstringSetFormat{latin}{\mkbibemph{#1}}%
}
\UndefineBibliographyExtras{british}{%
\UndeclareBibstringSet{latin}%
}
\addbibresource{biblatex-examples.bib}
\begin{document}
Lorem \autocite{aksin}
\printbibliography
\end{document}
It should be enough the redefine the name:andothers macro.
\renewbibmacro*{name:andothers}{%
\ifboolexpr{
test {\ifnumequal{\value{listcount}}{\value{liststop}}}
and
test \ifmorenames
}
{\ifnumgreater{\value{liststop}}{1}
{\finalandcomma}
{}%
\andothersdelim\bibstring[\mkandothers]{andothers}}
{}}
The only change to the default is that we have \bibstring[\mkandothers]{andothers}, so that the 'andothers' bibstring is wrapped in \mkandothers, that can be defined as
\newcommand*{\mkandothers}{\mkbibemph}
In total
\documentclass{article}
\usepackage[maxcitenames = 2]{biblatex}
\addbibresource{biblatex-examples.bib}
\newcommand{\mkandothers}{\mkbibemph}
\renewbibmacro{name:andothers}{%
\ifboolexpr{
test {\ifnumequal{\value{listcount}}{\value{liststop}}}
and
test \ifmorenames
}
{\ifnumgreater{\value{liststop}}{1}
{\finalandcomma}
{}%
\andothersdelim\bibstring[\mkandothers]{andothers}}
{}}
\begin{document}
\citeauthor{companion}
\printbibliography
\end{document}
