UI - fix edit azure public model name + fix editing model name post create

* test(test_router.py): add unit test confirming fallbacks with tag based routing works as expected

* test: update testing

* test: update test to not use gemini-pro

google removed it

* fix(conditional_public_model_name.tsx): edit azure public model name

Fixes https://github.com/BerriAI/litellm/issues/10093

* fix(model_info_view.tsx): migrate to patch model updates

Enables changing model name easily

tests/litellm/test_router.py

@@ -78,3 +78,43 @@ def test_router_with_model_info_and_model_group():
         model_group="gpt-3.5-turbo",
         user_facing_model_group_name="gpt-3.5-turbo",
     )
+
+
+@pytest.mark.asyncio
+async def test_router_with_tags_and_fallbacks():
+    """
+    If fallback model missing tag, raise error
+    """
+    from litellm import Router
+
+    router = Router(
+        model_list=[
+            {
+                "model_name": "gpt-3.5-turbo",
+                "litellm_params": {
+                    "model": "gpt-3.5-turbo",
+                    "mock_response": "Hello, world!",
+                    "tags": ["test"],
+                },
+            },
+            {
+                "model_name": "anthropic-claude-3-5-sonnet",
+                "litellm_params": {
+                    "model": "claude-3-5-sonnet-latest",
+                    "mock_response": "Hello, world 2!",
+                },
+            },
+        ],
+        fallbacks=[
+            {"gpt-3.5-turbo": ["anthropic-claude-3-5-sonnet"]},
+        ],
+        enable_tag_filtering=True,
+    )
+
+    with pytest.raises(Exception):
+        response = await router.acompletion(
+            model="gpt-3.5-turbo",
+            messages=[{"role": "user", "content": "Hello, world!"}],
+            mock_testing_fallbacks=True,
+            metadata={"tags": ["test"]},
+        )