Altering Bjornstrup chapter style so as to have rounded edges

Question

I would appreciate help in altering the chapter style of this document so that the grey backdrop has slightly rounded edges, and the horizontal space between the right edge of the backdrop and the words "A chapter" can be varied.

\documentclass[11pt,a4paper]{report}
\usepackage[margin=2.5cm]{geometry}
\usepackage{xcolor}
\usepackage[calcwidth]{titlesec}
\usepackage{blindtext}
\usepackage{scrextend}
\usepackage{microtype}
\usepackage[leqno]{amsmath}
\usepackage{etoolbox}
\usepackage{lipsum}
\usepackage[Bjornstrup]{fncychap} % <===================================



\colorlet{chapbgcolor}{gray!50}% shaded background color for chapters
\colorlet{chapnumcolor}{black!55}% color for numbers in chapters

\begin{document}
\sloppy
\chapter{A chapter}
Some text

\end{document}

Answer 1

Here is a quick attempt to produce something along those lines.

\documentclass[11pt,a4paper]{report}
\usepackage[margin=2.5cm]{geometry}
\usepackage{xcolor}
\usepackage[calcwidth]{titlesec}
\usepackage{microtype}
%\usepackage[Bjornstrup]{fncychap} % <===================================
\usepackage{tikz}


\colorlet{chapbgcolor}{gray!50}% shaded background color for chapters
\colorlet{chapnumcolor}{black!55}% color for numbers in chapters
%from https://tex.stackexchange.com/a/233830/121799
\newcommand{\chaptitle}[1]{%
\begin{tikzpicture}
\fill[chapbgcolor!70,rounded corners=5pt] (0,2.5) rectangle (\linewidth,0);
\node[align=right,anchor=south east,inner sep=6pt,font=\Large\bfseries\sffamily] at (\linewidth,0) {#1};
\node[font=\fontsize{60}{62}\usefont{OT1}{ptm}{m}{n}\selectfont\itshape\bfseries,text=chapnumcolor] at 
(\linewidth,2.5) {\thechapter};
\end{tikzpicture}
}

\titleformat{\chapter}[display]
{\normalfont\huge\bfseries\sffamily}{}{25pt}{\chaptitle}
\titlespacing*{\chapter} {0pt}{110pt}{20pt}


\begin{document}
\sloppy
\chapter{A chapter}


Some text

\end{document}