a radical has a couple of increasing sizes (discrete steps, if they have a slant depends of the font designer) before it switches to an extensible that then normally has no slant
Interesting. That explains the difference: The \rho made the radical big enough to switch to the extensible, unslanted version.
(in context one can hook in a mp variant that keeps the slant) (if needed we can make it an option to omit steps and always use upright)
My math-typography sense is far from developed, and mostly comes from having read lots of math books. With that caveat, my gut feelings are that (1) the switch from slant to upright is a bit surprising for a reader, and (2) that the slant version is more common, so an always-upright radical would also be a bit surprising. But perhaps you or others with a more developed typographical eye have a more principled way of judging? -Sanjoy