To access the DCP components from the broker using the Graphql DXA entity model - components should be published to the broker.
At least from sites 9.5, it's possible by data template less publishing to get that data from broker using Graphql.
I don't see any other option to fetch this information without publishing it as DCP.
Ended up going a different way. Instead of trying to get the labels/configuration externally, now I'm pushing them from DXA to the consuming applications.
Way to obtain the settings within DXA:
string websiteConfiguration = SiteConfiguration.ContentProvider.
IIRC, the DXA Model Service/Extension only sets EntityModelData.linkUrl for linked Components (nested Entity Models). However, when this property is not set, the DXA Web Application Framework should use the CD link resolving API to resolve the link.
If I look at the DXA.NET implementation (which I'm most familiar with), I see it checks if EntityModelData....