I went to test this on my game and noticed that my Xbox controller didn't work but SHIFT+TAB did bring up the Steam overlay. Realised that when I uploaded my last build I'd forgotten to add:
"allow-host-input-processing": false
to my package.json.
So I uploaded a new build with that option - XBox controller works but the overlay doesn't.
These are my settings in:
Steamworks Admin -> Application -> Steam Input
Opt Controllers into Steam Input:
Xbox, PlayStation, Nintendo Switch, Generic (DirectInput) & Any Future Devices
All Unchecked
Steam Input Default Controller Configuration
None Selected
So I _think_ it's the last option that's being discussed here but still don't have both the overlay and XBox controller working at the same time. But to be honest, all the Steam controller options confuse the hell out of me - but willing to test anything anyone can suggest.