Please, please contact Valve as your first port of call. There is very little we can do about it. It's all their software and we comply with all their documented requirements, which pretty much just say "it should work".
NW.js support for the overlay currently depends on hacky settings that are not officially supported, and in fact is currently broken in the latest NW.js releases. As it's not an officially supported feature, they are within their rights to say "sorry, that's not supported" and close the issue as 'won't fix'. So I really would not say that's working particularly well either and is not a reliable basis for a feature anyone cares about. If they fix it, it will basically be luck; if they don't, we're back to square one. To have robust support for the Steam overlay that consistently works, we need Valve's co-operation.
Having said that, try WebView2 in the latest beta if you haven't already - it contains a change that may help.