Unfortunately I cannot help you with the ESP8266 (never used it), but I have another project that uses a WiFi module from Microchip: https://www.hackster.io/msb4180/2wd-voice-controlled-robot-with-arduino-and-bitvoicer-server-310f9a. Maibe that can help your.

I have tested the code again and it is working fine. However, I do not remember for sure what the default UART rate is for the WiFi module. If it is 9600 bps and it is the first time you set up your module, you will have to change the UART rate in the first instruction: Serial.begin(115200) to Serial.begin(9600). Also make sure the shield switch is in the UART position after you upload the setup code to the Arduino.