fix(vertex_ai): strip a trailing slash from a custom Gemini api_base

A custom `api_base` for `gemini/*` was joined straight into the request path,
so the trailing slash that copying it out of Google's docs leaves behind
produced `.../openai//models/...`. Google answers that with a 404, which made
the model unreachable through the SDK.

The other two branches of `_check_custom_proxy` already strip it; the Gemini
branch was the one that did not.

Fixes #43828

litellm/llms/vertex_ai/vertex_llm_base.py

@@ -667,7 +667,9 @@ class VertexBase:
                 # For Gemini (Google AI Studio), construct the full path like other providers
                 if model is None:
                     raise ValueError("Model parameter is required for Gemini custom API base URLs")
-                url = f"{api_base}/models/{model}:{endpoint}"
+                # A trailing slash on api_base is a common copy-paste from the docs; without
+                # stripping it the joined path carries `//`, which Google answers with a 404.
+                url = f"{api_base.rstrip('/')}/models/{model}:{endpoint}"
                 if gemini_api_key is None:
                     raise ValueError(
                         "Missing Gemini API key. Set the GEMINI_API_KEY or GOOGLE_API_KEY environment variable."

tests/unit/llms/vertex_ai/test_vertex_llm_base.py

@@ -875,6 +875,47 @@ class TestVertexBase:
                 result_url == expected_url
             ), f"Expected {expected_url}, got {result_url} for model {model}"
 
+    def test_check_custom_proxy_gemini_url_strips_trailing_slash(self):
+        """A trailing slash on api_base must not double up in the joined path.
+
+        Copy-pasting the api_base from Google's docs leaves the slash in place,
+        and the resulting `//` is answered with a 404. #43828
+        """
+        vertex_base = VertexBase()
+
+        _, url = vertex_base._check_custom_proxy(
+            api_base="https://generativelanguage.googleapis.com/v1beta/openai/",
+            custom_llm_provider="gemini",
+            gemini_api_key="test-api-key",
+            endpoint="generateContent",
+            stream=False,
+            auth_header=None,
+            url="https://generativelanguage.googleapis.com/v1beta/models/gemini-3.8-flash:generateContent",
+            model="gemini-3.8-flash",
+        )
+
+        assert url == (
+            "https://generativelanguage.googleapis.com/v1beta/openai/models/gemini-3.8-flash:generateContent"
+        )
+        assert "//models" not in url
+
+    def test_check_custom_proxy_gemini_url_without_trailing_slash_is_unchanged(self):
+        """The slash-free form keeps producing the same URL it always did."""
+        vertex_base = VertexBase()
+
+        _, url = vertex_base._check_custom_proxy(
+            api_base="https://proxy.example.com/v1beta",
+            custom_llm_provider="gemini",
+            gemini_api_key="test-api-key",
+            endpoint="generateContent",
+            stream=False,
+            auth_header=None,
+            url="https://generativelanguage.googleapis.com/v1beta/models/gemini-2.5-pro:generateContent",
+            model="gemini-2.5-pro",
+        )
+
+        assert url == "https://proxy.example.com/v1beta/models/gemini-2.5-pro:generateContent"
+
     def test_check_custom_proxy_streaming_parameter(self):
         """Test that streaming parameter correctly adds ?alt=sse to URLs"""
         vertex_base = VertexBase()