@egreg I tried updating your answer to allow automatic scaling, but the solution cannot detect `\displaystyle`. Can this be fixed somehow?
```
\documentclass{article}
\usepackage{mathtools}
\ExplSyntaxOn
\DeclarePairedDelimiterX\set [2] \lbrace \rbrace
{
\mspace{1.5mu}
#1
\tl_if_blank:nF { #2 } { \mathrel{\dashedsep{#1}{#2}{\delimsize}} #2 }
\mspace{1.5mu}
}
\ExplSyntaxOff
\makeatletter
\newcommand{\dashedsep}[3]{%
\sbox0{$\m@th\left.#1#3\vert#2\right.$}%
\vcenter to \dimexpr \ht0+\dp0 {\offinterlineskip