The SoftwareSerial library running on an Uno can’t emulate a serial port which will run successfully at this sort of baud rate. The Uno simply doesn’t have the processing power to make this work consistently.
The solution is to configure your ESP-01 to communicate at a lower baud rate (9600 preferably) and use the same baud rate as your ESP8266_BAUD in your sketch.
Alternatively, you can use the UNO’s hardware serial port for communication with the ESP-01 (the hardware serial port is capable of much higher baud rates) and use a software serial port at 9600 for debugging. The problem with this approach is that you then need a TTL to USB adapter (an FTDI adapter) to allow you to view the serial debug messages on your computer.
A slightly better approach is to use a Mega, which has 3 hardware serial ports.
An even better approach is to throw the Arduino and ESP-01 combination in the bin and use a WiFi capable board such as the NodeMCU or ESP32.
More info on serial ports here…
Pete.