Serial.write(some_byte) writes a byte on the serial output. The Arduino serial monitor tries to interpret the bytes it receives as text:

• 0x11 is a control character, displayed as “□”
• 0x22 is the ASCII code for the double quote (")
• 0x33 is the ASCII code for the digit 3.
• 0x44 is the ASCII code for the uppercase letter “D”
• etc.

As mentioned in the comments, don't use multi-character constants (the ones you used, with single quotes); they might kill puppies. Single quotes are for character constants, like 'a'.

You can use strings (with double quotes), or real binary numbers without trickery; the latter will print without leading zeros.

This code example does both, so pick what you need:

const char* array1[] = {"0000", "0001", "0010", "0011"}; // strings
uint8_t array2[] = {0b000, 0b0001, 0b0010, 0b0011};      // binary numbers
int arraySize = sizeof(array1) / sizeof(array1[0]);
    
void setup() {
  Serial.begin(9600);
  while (!Serial);
    
  Serial.println("Print the strings:");  
  int i = 0;
  while (i < arraySize){
    Serial.println(array1[i]);
    i++;
  }
      
  Serial.println("\nPrint the binary numbers (note: no leading zeroes):");
  i = 0;
  while (i < arraySize){
    Serial.println(array2[i], BIN);
    i++;
  }
      
}
    
void loop() {
}

You can’t print an array in that way.

If you want to print an array of hexadecimal value (with two digits), you have to use sprintf function and change declaration of b array.

uint8_t b[]= {0x7E, 0x00, 0x1C, 0x90, 0x00, 0x13, 0XA2, 0x00, 
              0x41, 0x58, 0x1C, 0xCB, 0xFF, 0xFE, 0xC1, 0x7C, 
              0x00, 0x0F, 0x00, 0x01, 0x00, 0x00, 0x37, 0x46, 
              0x46, 0x46, 0x00, 0x00, 0x00, 0xE7};
int i;

void printHex(uint8_t num) {
  char hexCar[2];

  sprintf(hexCar, "%02X", num);
  Serial.print(hexCar);
}

void setup() {
  Serial.begin(9600);
}

void loop() {
  for(i=0; i<sizeof(b); i++){
    printHex(b[i]);
 }

 Serial.println();
 delay(500);
}

The output produced is:

7E001C900013A20041581CCBFFFEC17C000F0001000037464646000000E7 7E001C900013A20041581CCBFFFEC17C000F0001000037464646000000E7 7E001C900013A20041581CCBFFFEC17C000F0001000037464646000000E7