Getting one word only to blink

and

is somehow contradictory.

Post the last version of your sketch, in a new post, in code tags,
previously formatted with ctrl-T in the IDE.

Half an hour later...

So get your spoon ready and switch the brain off, if it was on. :upside_down_face:

#include <LiquidCrystal_I2C.h>

uint16_t x = 0;
const uint8_t input = A0;
bool smiliesVisible = true;
uint32_t lastSwap;
LiquidCrystal_I2C lcd(0x27, 16, 2);

void setup() {
  pinMode(input, INPUT_PULLUP);
  lcd.init();
  lcd.backlight();
  lcd.setCursor(0, 0);
  lcd.print(F(" ROUND COUNTER "));
  lcd.setCursor(0, 1);
  lcd.print(x);
  lcd.print(F(" = SMILIES "));
}

void loop() {
  bool intputActive = digitalRead(input) == LOW;
  if (intputActive ) {
    lcd.setCursor (0, 1);
    lcd.print(++x);
  }
  if (millis() - lastSwap >= 250) {
    lastSwap = millis();
    lcd.setCursor(lenNum(x), 1);
    lcd.print(smiliesVisible ? F("          ") : F(" = SMILIES"));
    smiliesVisible = not smiliesVisible;
  }
}

uint8_t lenNum(uint16_t check) {
  if (check < 10) {
    return 1;
  }
  if (check < 100) {
    return 2;
  }
  if (check < 1000) {
    return 3;
  }
  if (check < 10000) {
    return 4;
  }
  return 5;
}