This is a tutorial on your board.
https://forum.arduino.cc/t/atmega328p-esp8266-wifi-tutorial/944380
You need to do the trouble shooting to determine if you have a hardware issue with the Arduino to Nextion connection or if there is an issue with your syntax for the Nextion.
I have Arduino Uno WiFi ESP8266, I have power supply 6V, 2A, for both, so the GND is same, Arduino TX1 + Nextion RX, Arduino RX1 + Nextion TX.
How is 6v being applied to the Arduino? How is the Nextion being powered? Are you certain about the cross connection between the rx/tx wires.
Do you have another Arduino you can use to test the software serial function on your board?
Regarding the syntax of communication to the Nextion there have been many reported issues with using "Nextion.h".
It would be better to use either the methods of Perry Bebbington documented in
https://forum.arduino.cc/t/using-nextion-displays-with-arduino/580289
or alternatively the EasyNextionLibrary by Seithan which is available through the library manager.
https://github.com/Seithan/EasyNextionLibrary/tree/master
You will not find much support on this Arduino forum for using the ITEAD Nextion.h library.