I haven’t tried the first point but for me the PNG still exhibited incorrect colors.
Color Issues
I rarely use or follow the development of Inkscape anymore, but my impression is that it is fairly color management agnostic. There are a few controls in the GUI but they don’t do anything yet, unless I missed a new development. Stripping the metadata only worsens the situation if proper management exists, unless the metadata is incorrect in the first place. Moreover, PNG color profiling is still uncommon.
I wasn’t referring to the assigning or recognition of metadata but how Inkscape manipulates and handles (“manages”) the actual data. Anyway, color is a difficult nut to crack. @Elle’s website may help clarify some issues at play, though she focuses on raster processing.
Lastly, feel free to file a bug report, but I feel that we don’t have enough info to warrant proper attention. I suggest you bring this up in places where Inkscape developers are carrying out active conversation. As I don’t see an Inkscape Category on this forum, this might not be the best place to get results 