[web_server] Increase httpd task stack size to prevent stack overflow (#14997)

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

esphome/components/web_server_idf/web_server_idf.cpp

@@ -120,7 +120,10 @@ void AsyncWebServer::begin() {
   if (this->server_) {
     this->end();
   }
+  // Default httpd stack is defined by ESP-IDF. Increase to accommodate SerializationBuffer's
+  // 640-byte stack buffer used by web_server JSON request handlers.
   httpd_config_t config = HTTPD_DEFAULT_CONFIG();
+  config.stack_size = config.stack_size + 256;
   config.server_port = this->port_;
   config.uri_match_fn = [](const char * /*unused*/, const char * /*unused*/, size_t /*unused*/) { return true; };
   // Always enable LRU purging to handle socket exhaustion gracefully.