Add datetime date entities (#6191)

Co-authored-by: Jesse Hills <3060199+jesserockz@users.noreply.github.com>

esphome/components/api/api_server.cpp

@@ -255,6 +255,15 @@ void APIServer::on_number_update(number::Number *obj, float state) {
 }
 #endif
 
+#ifdef USE_DATETIME_DATE
+void APIServer::on_date_update(datetime::DateEntity *obj) {
+  if (obj->is_internal())
+    return;
+  for (auto &c : this->clients_)
+    c->send_date_state(obj);
+}
+#endif
+
 #ifdef USE_TEXT
 void APIServer::on_text_update(text::Text *obj, const std::string &state) {
   if (obj->is_internal())