If we look at the definitions of \bigl and \bigr, we find
\def\bigl{\mathopen\big}
\def\bigr{\mathclose\big}
In other words, \bigl<bracket> is equivalent to \mathopen\big<bracket>.
And yet mathtools (as explained on page 30 of its manual) uses the following constructions, at least when nostarscaled is activated:
\mathopen{<size><bracket>}
\mathclose{<size><bracket>}
And the manual actually stresses that these braces make a difference, at least in some fonts. Also, @egreg uses the same solution here. But why is the following not more correct?
\mathopen<size><bracket>
\mathclose<size><bracket>
mathtoolsmanual as well as this question, it does make a difference for the positioning of indices. (That being said, the provided answers seem to contradict themselves and each other, so I’m not entirely sure what exactly is going wrong.) Where do these positioning issues come from then, if the two constructions are close to equivalent? – Gaussler Aug 16 '21 at 09:18