Okay, you’re using your ESP-01 and Uno in a rather unconventional way, with the ESP running the sketch that you’ve included above.
Normally, people would use the ESP-01 as a Wi-Fi modem for the Uno, and have the ESP-01 running the factory default “AT” software and upload their sketch to the Uno. In that scenario, the Uno would be using the BlynkSimpleShieldEsp8266.h library and connecting the ESP-01 via a SoftwareSerial port.
When used in this way, the Uno’s large USB connector (which is connected to Serial) would be used as the debug port and #define BLYNK_PRINT Serial would send information to the serial monitor about the Blynk connection, ping time etc.
By including #define BLYNK_PRINT Serial in your ESP-01 sketch you are telling the Blunk library to send all of this data to the Serial port on your ESP-01, which is obviously tying-up that port.
Changing this to #define BLYNK_PRINT Serial1 is telling the Blynk library to send this data to the (non-existent) Serial1 port of your ESP-01. Personally, I’m somewhat surprised that this compiles, but to be honest, the best thing would be to remove this line altogether as it serves no purpose with your setup.
Actually, the best thing to do would be to replace the ESP-01 with a NodeMCU or Wemos D1 Mini and throw the ESP-01 and Uno in the scrap box.
Pete.