Shortauthor and authoryear-icomp: Use full author name for first citation like apa style

Question

I am using the authoryear-icomp biblatex style. For some publications by institutions with long names, I would like to use shortauthor. However, the style authoryear-icomp simply uses shortauthor from the first citation onwards, like so:

I would like it to work as it does in style=apa, which uses the full author name for the first citation and introduces the short name in square brackets, which it then uses for all further citations (even for other publications of the same author).

This is the output if I change the style to apa:

Is there any way to achieve this behaviour with authoryear-icomp?

This is the MWE:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}

\usepackage[style=authoryear-icomp, % alternatively: style=apa
  bibstyle=authoryear,
  autocite=inline,
  backend=biber
  ]
 {biblatex}

\usepackage{filecontents}

\begin{filecontents*}{testbib.bib}

@online{test1,
  author = {{Institution Long Name}},
  shortauthor = {ILN},
  title = {Test title},
  year = {2020}
}

@online{test2,
  author = {{Institution Long Name}},
  shortauthor = {ILN},
  title = {Another test title},
  year = {2020}
}

\end{filecontents*}

\addbibresource{testbib.bib}


\begin{document}

Citation number one \autocite{test1}.

Citation number two \autocite{test1}.

Third citation with a different publication by the same author \autocite{test2}.

\end{document}

Answer 1

You can do something like this - I took some code from APA style. You may need to make this more in line with cite from the authoryear-icomp style for more general use but this gets you what you want as a start:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}

\usepackage[style=authoryear-icomp, % alternatively: style=apa
  bibstyle=authoryear,
  autocite=inline,
  backend=biber
  ]
 {biblatex}

\usepackage{filecontents}

\begin{filecontents*}{testbib.bib}

@online{test1,
  author = {{Institution Long Name}},
  shortauthor = {ILN},
  title = {Test title},
  year = {2020}
}

@online{test2,
  author = {{Institution Long Name}},
  shortauthor = {ILN},
  title = {Another test title},
  year = {2020}
}

\end{filecontents*}

\addbibresource{testbib.bib}

\makeatletter
\DeclareCiteCommand{\parencite}[\mkbibparens]
  {\usebibmacro{cite:init}%
   \usebibmacro{prenote}}
  {\usebibmacro{citeindex}%
   \usebibmacro{metacite}%
   \usebibmacro{cite:post}}
  {}
  {\usebibmacro{cite:postnote}}

\newbibmacro*{cite:post}{%
  \xifinlist{\thefield{fullhash}}{\cbx@names}
    {}
    {\listxadd{\cbx@names}{\thefield{fullhash}}}}

\global\let\cbx@names\@empty
\def\cbx@ifnamesaved{%
  \xifinlist{\thefield{fullhash}}{\cbx@names}
    {\@firstoftwo}
    {\@secondoftwo}}

\newbibmacro*{metacite}{%
  \ifnameundef{shortauthor}
    {\usebibmacro{cite}}
    {\usebibmacro{sacite}}}

\newbibmacro*{sacite}{%
  \cbx@ifnamesaved
    {\printnames{shortauthor}}
    {\printnames{author}%
     \addspace\mkbibbrackets{\printnames[sabrackets]{shortauthor}}}%
  \setunit{\printdelim{nameyeardelim}}%
  \usebibmacro{cite:labeldate+extradate}%
  \savefield{namehash}{\cbx@lasthash}%
  \savefield{labelyear}{\cbx@lastyear}%
  \setunit{\multicitedelim}}

\makeatother

\begin{document}

Citation number one \autocite{test1}.

Citation number two \autocite{test1}.

Third citation with a different publication by the same author \autocite{test2}.

\end{document}