This is not a workaround and \r{A} is a LaTeX text command, which is not valid in math mode. You could use the \mathring{A} in formulas instead, or add $\newcommand{\r}[1]{\mathring{#1}}$ to redefine \mathring{...} to \r{...}, but you still need to put it inside the \pu{...} command to be rendered properly as a unit.
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