Consider this appsettings.json:
appsettings.json
{ \"Parent\": { \"ChildOne\": \"C1 from secrets.json\", \"ChildTwo\": \"C2 from secrets.json\" } }
After more experimentation than I'd like to admit I think I have the answer.
Where you use : on an App Service, use a __ (double underscore) on an App Service with containers.
:
__
So Parent__ChildOne instead of Parent:ChildOne.
Parent__ChildOne
Parent:ChildOne