Should focus on String.new not String#initialize.

core/string.rbs

@@ -703,7 +703,7 @@ class String
   #
   #     String.new('hello', encoding: 'UTF-8', capacity: 25)
   #
-  def initialize: (?string source, ?encoding: encoding?, ?capacity: int?) -> self
+  def initialize: (?string source, ?encoding: encoding, ?capacity: int) -> void
 
   # <!--
   #   rdoc-file=string.c

test/stdlib/String_test.rb

@@ -7,6 +7,26 @@ class StringSingletonTest < Test::Unit::TestCase
 
   testing 'singleton(::String)'
 
+  def test_new
+    assert_send_type  '() -> String',
+                      String, :new
+
+    with_string do |source|
+      assert_send_type  '(string) -> String',
+                        String, :new, source
+    end
+
+    with_encoding do |encoding|
+      assert_send_type  '(encoding: encoding) -> String',
+                        String, :new, encoding: encoding
+    end
+
+    with_int do |capacity|
+      assert_send_type  '(capacity: int) -> String',
+                        String, :new, capacity: capacity
+    end
+  end
+
   def test_try_convert
     assert_send_type  '(String) -> String',
                       String, :try_convert, 'foo'
@@ -73,26 +93,6 @@ def assert_case_method!(method, normal:, nochange:, include_fold: false)
                       nochange.dup, method, :turkic, :lithuanian
   end
 
-  def test_initialize
-    assert_send_type  '() -> String',
-                      String.allocate, :initialize
-
-    with_string do |source|
-      assert_send_type  '(string) -> String',
-                        String.allocate, :initialize, source
-    end
-
-    with_encoding.and_nil do |encoding|
-      assert_send_type  '(encoding: encoding?) -> String',
-                        String.allocate, :initialize, encoding: encoding
-    end
-
-    with_int.and_nil do |capacity|
-      assert_send_type  '(capacity: int?) -> String',
-                        String.allocate, :initialize, capacity: capacity
-    end
-  end
-
   def test_initialize_copy
     test_replace(:initialize_copy)
   end