providers/*: add assigned application name and slug

authentik/core/api/providers.py

@@ -1,4 +1,5 @@
 """Provider API Views"""
+from rest_framework.fields import ReadOnlyField
 from rest_framework.serializers import ModelSerializer, SerializerMethodField
 from rest_framework.viewsets import ModelViewSet
 
@@ -44,6 +45,10 @@ class ProviderViewSet(ModelViewSet):
     filterset_fields = {
         "application": ["isnull"],
     }
+    search_fields = [
+        "name",
+        "application__name",
+    ]
 
     def get_queryset(self):
         return Provider.objects.select_subclasses()