Mega2560 + ESP8266 + MQTT (PubSubClient error)

Personally, I’s use Blynk or MQTT on your device, not both.
If you do need to use both then you should set-up your Wi-Fi connection using a different library then use Blynk.config and Blynk.connect rather than Blynlk.begin.

https://docs.blynk.cc/#blynk-firmware

I use Blynk and MQTT extensivly, but Use Node-Red and Mosquitto running on a Pi and only run MQTT code on my ESP devices.

If you want a proper touch screen then I’d forget the Arduino shield and go with a Nextion connected to an ESP.

Pete.