Your problem can be illustrated by primitive construct:
$[\mathop{[[[[]]]]}\limits^{[[[[]]]]}_{[[[[]]]]}]$
Indeeed, the above kern is smaller than the bellow kern. The appendix G of The TeXbook, paragraph 13a, says that the above kern is max(xi9, xi11-dp) and below kern is max (xi10, xi12-ht). The values from Computer Modern are:
xi9 = \fontdimen9\textfont3 = 1.11111pt
xi10 = \fontdimen10\textfont3 = 1.66666pt
xi11 = \fontdimen11\textfont3 = 1.99998pt
xi12 = \fontdimen12\textfont3 = 6.0pt
dp = \dp\hbox{$\scriptstyle[]$} = 1.75pt
ht = \ht\hbox{$\scriptstyle[]$} = 5.25pt
We can see that the above maximum is xi9 and below maximum is xi10. So, we have kern above 1.11111pt and kern below 1.66666pt.
You can set better kern above by
\fontdimen9\textfont3=1.666666pt
Then you have the same kern above and below. Tested by pdftex document.
If we are using luatex, then setting the \fontdimen is irrelevant and we must to use LuaTeX primitive instead:
\Umathlimitabovevgap\textstyle=1.6666666pt
Tested by luatex document or optex document.
I tested the Unicode-math of LatinModern font too and I have found that the bug from Computer Modern is corrected here, the kern above and below are set uniformly to 1.666666pt. So, you can use Unicode-math Latin Modern to solve your problem.
\undersetwith\stackrelwill 1) make always a Rel atom whether you want it or not, and 2) give possibly unexpected results if you use this combination for single letters. It would be better to nest\oversetwith\underset, or with a recentamsmathyou could simply use\overunderset. – campa Nov 11 '22 at 08:59