With version 3 of acro the way the list styles (now called templates) are defined has changed completely – this happened to make the whole process more flexible and more customisable. The drawback is that it is not compatible with the way it was done in version 2. Just renaming the command will not do as you have discovered.
Quite some part of the manual describes how templates can be defined and modified. In your case it is actually not very difficult to adapt the layout you had:
\documentclass[12pt]{report}
\usepackage{acro}
\usepackage{enumitem}
\newlength\myitemwidth
\setlength\myitemwidth{5em}
\newlist{listabbrev}{description}{1}
\setlist[listabbrev]{
labelindent = 0pt,
labelsep = 0pt,
leftmargin = \myitemwidth,
labelwidth = \myitemwidth,
format = \normalfont
}
\NewAcroTemplate[list]{styleabbrev}{%
\let\description\listabbrev
\let\enddescription\endlistabbrev
\UseAcroTemplate[list]{description}[0]%
}
\acsetup{
list/template = styleabbrev,
list/heading = chapter*,
list/name = Abkürzungen
}
\DeclareAcronym{EEG}{
short = EEG,
long = Erneuerbare-Energien-Gesetz,
}
\DeclareAcronym{dbms}{
short = DBMS,
long = Database Management System,
}
\begin{document}
\printacronyms
\acuseall
\end{document}

The layout in the picture you posted is a little different. The following code demonstrates how a template based on a longtable could be defined which simulates this layout:
\documentclass[12pt]{report}
\usepackage{acro}
\usepackage{longtable,array}
\newlength\abbrevwidth
\setlength\abbrevwidth{6em}
\setlength\LTleft{0pt}
\setlength\LTright{0pt}
\NewAcroTemplate[list]{styleabbrev}{%
\AcroNeedPackage{array,longtable}%
\acronymsmapF{%
\AcroAddRow{%
\acrowrite{short}%
\acroifT{alt}{/}\acrowrite{alt}%
&
\acrowrite{list}%
\acroifanyT{foreign,extra}{ (}%
\acrowrite{foreign}%
\acroifallT{foreign,extra}{, }%
\acrowrite{extra}%
\acroifanyT{foreign,extra}{)}%
\acropagefill
\acropages
{\acrotranslate{page}\nobreakspace}
{\acrotranslate{pages}\nobreakspace}%
\tabularnewline
}
}{\AcroRerun}
\acroheading
\acropreamble
\par\noindent
\begin{longtable}{@{}p{\abbrevwidth}p{\dimexpr\linewidth-\abbrevwidth-2\tabcolsep\relax}@{}}
\bfseries Abkürzung & \bfseries Erläuterung \endhead
\AcronymTable
\end{longtable}
}
\acsetup{
list/template = styleabbrev,
list/heading = chapter*,
list/name = Abkürzungsverzeichnis
}
\DeclareAcronym{EEG}{
short = EEG,
long = Erneuerbare-Energien-Gesetz,
}
\DeclareAcronym{dbms}{
short = DBMS,
long = Database Management System,
}
\begin{document}
\printacronyms
\acuseall
\end{document}

\NewAcroTemplate[list], see section 23.5 of theacropackage manual on page 41. – Marijn Jul 02 '20 at 11:50\DeclareAcroListStyle{styleabbrev}{list}{list = listabbrev}with\NewAcroTemplate[list]{styleabbrev}it simply won't print anything regarding the abbreviations... clearly there is something wrong. – TeXlearner Jul 03 '20 at 10:35