As far as I've understood the step argument of fuzzy shadow is a shrink offset and the vertical shift divided by the step size should give the number of individual shadows being drawn.
If the shift is given in pt, it's perhaps better to provide the same length unit for the step as well.
I've used 0.4pt to provide for 10 'shadows':
\documentclass[10pt,twoside]{article}\usepackage[utf8]{inputenc}\usepackage{lipsum}\usepackage[most]{tcolorbox}\usepackage{tikz}\definecolor{bgtan}{HTML}{F7F2E5}\pagecolor{bgtan}\newtcolorbox{paperbox}[1][]{ frame hidden, enhanced, boxrule=0pt, boxsep=0.25ex, arc=0mm, borderline north={1pt}{-0.5pt}{black}, borderline south={1pt}{-0.5pt}{black}, colback=black!20!white, colframe=black!20!white, fuzzy shadow={0mm}{-4pt}{-0.5pt}{0.4pt}{black!60!white}, #1}\begin{document}\begin{paperbox} \lipsum[1]\end{paperbox}\end{document}
