csquotes: always enclose blockquote in " "

The csquotes manual suggests to redefine \mkblockquote, see section 8.7 Hooks for Quotations and Citations. One possibility would be

\renewcommand\mkblockquote[4]{\enquote{#1#2#3}#4}

which gives the same effect as in this answer.

The four arguments of \mkblockquote refer to

\mkblockquote{<text>}{<punct>}{<tpunct>}{<cite>}

which are explained in the manual as follows

• #1 The text argument of the command.
• #2 The optional <punct> argument of the command. If there is no <punct> argument, this parameter is empty.
• #3 Trailing <tpunct> punctuation immediately after the command. If there is no such punctuation or if the autopunct feature is disabled, this parameter is empty.
• #4 The optional <cite> argument of the command, wrapped in \mkcitation. If there is no <cite> argument, this parameter is empty. With integrated quotation commands, this parameter is the citation code, wrapped in \mkccitation.

In the example below I use

\renewcommand\mkblockquote[4]{\leavevmode\llap{,,}#1#2#3``#4}

where \llap{,,} places the opening quotation mark left of the text in the quote margin. (The space at the end before the closing quotation mark is an artefact of \blindtext and not related to \mkblockquote.)

\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[ngerman]{babel}
\usepackage{lmodern,blindtext}

\usepackage[babel=true,strict=true,german=quotes,threshold=1]{csquotes}

\renewcommand\mkblockquote[4]{\leavevmode\llap{,,}#1#2#3``#4}

\begin{document}

\blindtext

\blockquote{\blindtext}

\blindtext

\end{document}

Just add \enquote{...} inside the \blockquote command.

MWE:

\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[ngerman]{babel}
\usepackage{lmodern,blindtext}

\usepackage[babel=true,strict=true,german=quotes,threshold=1]{csquotes}

\begin{document}
\blindtext

\blockquote{\enquote{\blindtext}}   %<=======================

\blindtext
\end{document}

Result: