You would need to create the background service using IHostedService which runs every time to look for endpoints in controller by registering the service builder.Services.AddEndpointsApiExplorer and get the service inside the background job using,
var apiProvider = scope.ServiceProvider.GetRequiredService<IApiDescriptionGroupCollectionProvider>();
use the apiProvider to retrieve the collection group by controller and prepare the all list of endpoints collections it calls the postman update collection api and post body to https://api.getpostman.com/collections/{CollectionUid} to your postman collections.

Let me know If you want full implementation of the code, I will do it

Thanks