With Inkscape 1.x I see squares or blocks instead of readable text in the notification area and the input boxes when working under Windows 10. Does anyone know which font Inkscape is using to render these elements of the UI?

I believe this is a known issue, and I think it's not about fonts but about languages.

Can you look in the issue tracker at https://inkscape.org/report? Please look through the list for 'all' issues, including the closed ones. Closing only means that they've been triaged and moved to the developers' bug tracker.