This seems to be a roadblock that cannot be worked around. Webview2 could become a solution in the future when it's ready for multi-platform distribution but the NWjs side of things looks pretty bad.
It would either require Valve to add very specific support for "fake" Chromium window titlebars or Chromium to offer a version of their custom titlebar that integrates with the native Windows DWM.
Their recently added Windows 11 mica titlebar support doesn't seem to fix this issue either and it would be useless on Windows 10 anyway. NWjs will probably never support Mica to be begin with but it was worth a shot I suppose.
TL;DR:
- Valve: Doesn't care enough to implement specific workaround.
- Google/Chromium: Doesn't care about issues for 3rd party projects that use their browser engine.
The Steam overlay is usually not picked up by streaming software anyway. So it's only a slight inconvenience for players who prefer playing in windowed mode for the time being.