Everywhere: Rename to_{string => deprecated_string}() where applicable

This will make it easier to support both string types at the same time
while we convert code, and tracking down remaining uses.

One big exception is Value::to_string() in LibJS, where the name is
dictated by the ToString AO.

Userland/Libraries/LibJS/Runtime/Intl/ListFormat.cpp

@@ -274,7 +274,7 @@ ThrowCompletionOr<Vector<DeprecatedString>> string_list_from_iterable(VM& vm, Va
             }
 
             // iii. Append nextValue to the end of the List list.
-            list.append(next_value.as_string().string());
+            list.append(next_value.as_string().deprecated_string());
         }
     } while (next != nullptr);