feat: add list_functions client APIs (#4108)

Function registration and exact lookup are exposed through the SDK, but
clients cannot discover published versions even though the server
provides `POST /v1/functions/list`.

Add Rust and Python sync/async `list_functions()` APIs that return typed
`FunctionVersion` values. The remote client requests canonical
definitions and follows opaque page tokens until the listing is
complete, including empty intermediate pages, while preserving the
server's name/version ordering. Local databases retain the existing
Function-catalog unsupported error.

The SDK consumes protocol pagination internally so callers receive the
complete catalog rather than handling server-specific page tokens.

python/python/tests/test_first_class_function_slice2.py

@@ -1017,6 +1017,8 @@ def test_local_function_catalog_operations_are_not_supported(tmp_path):
         db.create_function_async(normalize_score)
     with pytest.raises(NotImplementedError, match=message):
         db.get_function("normalize_score", version="fv_exact")
+    with pytest.raises(NotImplementedError, match=message):
+        db.list_functions()
     with pytest.raises(NotImplementedError, match=message):
         db.drop_function("normalize_score", version="fv_exact")
 
@@ -1064,6 +1066,22 @@ def _mock_remote_function_catalog():
                     "version": "fv_exact",
                 }
                 response = state["version"]
+            elif self.path == "/v1/functions/list":
+                assert body["include_definition"] is True
+                if "page_token" not in body:
+                    response = {
+                        "functions": [
+                            {
+                                "name": "normalize_score",
+                                "version": "fv_exact",
+                                "definition": state["version"],
+                            }
+                        ],
+                        "page_token": "next",
+                    }
+                else:
+                    assert body["page_token"] == "next"
+                    response = {"functions": []}
             elif self.path == "/v1/functions/drop":
                 assert body == {
                     "name": "normalize_score",
@@ -1130,6 +1148,49 @@ def test_blocking_remote_registration_returns_function_version():
     ]
 
 
+def test_remote_list_functions_paginates_and_returns_typed_versions():
+    with _mock_remote_function_catalog() as (host, state):
+        db = lancedb.connect(
+            "db://dev",
+            api_key="fake",
+            host_override=host,
+            client_config={"retry_config": {"retries": 0}},
+        )
+        created = db.create_function(normalize_score)
+        state["requests"].clear()
+        functions = db.list_functions()
+
+    assert functions == [created]
+    assert state["requests"] == [
+        ("/v1/functions/list", {"include_definition": True}),
+        (
+            "/v1/functions/list",
+            {"include_definition": True, "page_token": "next"},
+        ),
+    ]
+
+
+@pytest.mark.asyncio
+async def test_async_remote_list_functions_returns_typed_versions():
+    with _mock_remote_function_catalog() as (host, state):
+        db = await lancedb.connect_async(
+            "db://dev",
+            api_key="fake",
+            host_override=host,
+            client_config={"retry_config": {"retries": 0}},
+        )
+        registration = await db.create_function_async(normalize_score)
+        created = await registration.wait()
+        state["requests"].clear()
+        functions = await db.list_functions()
+
+    assert functions == [created]
+    assert [path for path, _ in state["requests"]] == [
+        "/v1/functions/list",
+        "/v1/functions/list",
+    ]
+
+
 def test_remote_drop_function_sends_exact_version():
     with _mock_remote_function_catalog() as (host, state):
         db = lancedb.connect(