\documentclass{article}

\usepackage{hyperref}

\usepackage[
  accsupp,
  abbreviations,
  shortcuts=abbr,
  % debug=showaccsupp,
]{glossaries-extra}

\makeglossaries

% I'm redefining for the intended use case (copy-paste of uppercased small
% caps abbreviations), but the problem also happens without this redefinition,
% as is visible with 'debug=showaccsupp'.
\renewcommand*{\glsshortaccsupp}[2]{\glsaccessibility{ActualText}{#1}{#2}}

\setabbreviationstyle[initialism]{long-short-sc}
\setabbreviationstyle{long-only-short-only}

\pdfstringdefDisableCommands{\renewcommand*{\glstextup}{}}

\newabbreviation[
  category=initialism,
  shortaccess={ABC},
]{ABC}{abc}{Aaaa Bbbb Cccc}

\newabbreviation{Dr}{Dr.}{Doctor}

\begin{document}

\ab{ABC}, \ab{ABC}, \ab{ABC}

\ab{Dr}, \ab{Dr}, \ab{Dr}

\end{document}
