Once again, I will post what I tried based on this sample.
M5.begin () and M5.Power.begin () are recognitions that are unnecessary in M5Camera. When enabled and execed, it stopped at the log "M5Stack Initialize ..".Therefore, comment outed.

#include <Wire.h>
#include "MFRC522_I2C.h"
#include <M5Stack.h>

// 0x28 is i2c address on SDA. Check your address with i2cscanner if not match.
MFRC522 mfrc522 (0x28); // Create MFRC522 instance.

void setup () {
  //M5.begin ();
  //M5.Power.begin ();

  Serial.begin (115200); // Initialize serial communications with the PC
  Wire.begin (); // Initialize I2C

  Serial.println (F ("PCD_Init () Start"));
  mfrc522.PCD_Init (); // Init MFRC522
  Serial.println (F ("PCD_Init () Finish"));
  ShowReaderDetails (); // Show details of PCD-MFRC522 Card Reader details
  Serial.println (F ("Scan PICC to see UID, type, and data blocks ..."));
}

void loop () {
  // Look for new cards, and select one if present
  if (! mfrc522.PICC_IsNewCardPresent () ||! mfrc522.PICC_ReadCardSerial ()) {
    delay (50);
    return;
  }

  // Now a card is selected.The UID and SAK is in mfrc522.uid.

  // Dump UID
  Serial.print (F ("Card UID:"));
  for (byte i = 0; i <mfrc522.uid.size; i ++) {
    Serial.print (mfrc522.uid.uidByte [i] <0x10? "0": "");
    Serial.print (mfrc522.uid.uidByte [i], HEX);
  }
  Serial.println ();

}

void ShowReaderDetails () {
  // Get the MFRC522 software version
  byte v = mfrc522.PCD_ReadRegister (mfrc522.VersionReg);
  Serial.print (F ("MFRC522 Software Version: 0x"));
  Serial.print (v, HEX);
  if (v == 0x91)
    Serial.print (F ("= v1.0"));
  else if (v == 0x92)
    Serial.print (F ("= v2.0"));
  else
    Serial.print (F ("(unknown)"));
  Serial.println ("");
  // When 0x00 or 0xFF is returned, communication probably failed
  if ((v == 0x00) || (v == 0xFF)) {
    Serial.println (F ("WARNING: Communication failure, is the MFRC522 properly connected?"));
  }
}

Serial output stops with “PCD_Init () Start”. When PCD_Init () is confirmed, it seems to be infinite loop in the following while ().

void MFRC522 :: PCD_Reset () {
PCD_WriteRegister (CommandReg, PCD_SoftReset); // Issue the SoftReset command.
// The datasheet does not mention how long the SoftRest command takes to complete.
// But the MFRC522 might have been in soft power-down mode (triggered by bit 4 of CommandReg)
// Section 8.8.2 in the datasheet says the oscillator start-up time is the start up time of the crystal + 37,74�s.Let us be generous: 50ms.
delay (50);
// Wait for the PowerDown bit in CommandReg to be cleared
while (PCD_ReadRegister (CommandReg) & (1 << 4)) {
// PCD still restarting-unlikely after waiting 50ms, but better safe than sorry.
}
} // End PCD_Reset ()

I also found that the following logs continue to appear.

15:01:09.879 -> [I][esp32-hal-i2c.c:1130] i2cProcQueue(): Bus busy, reinit
15:01:09.924 -> [I][esp32-hal-i2c.c:1130] i2cProcQueue(): Bus busy, reinit
15:01:09.968 -> [I][esp32-hal-i2c.c:1130] i2cProcQueue(): Bus busy, reinit
...

#include <Wire.h>
#include "MFRC522_I2C.h"
#include <M5Stack.h>

// 0x28 is i2c address on SDA. Check your address with i2cscanner if not match.
MFRC522 mfrc522(0x28);   // Create MFRC522 instance.

void setup() {
  M5.begin();
  M5.Power.begin();
  M5.Lcd.fillScreen( BLACK );
  M5.Lcd.setCursor(0, 0);
  M5.Lcd.setTextColor(YELLOW);  
  M5.Lcd.setTextSize(2);

  M5.Lcd.fillScreen( BLACK );
  M5.Lcd.setCursor(0, 0);
  M5.Lcd.println("M5StackFire MFRC522");
  Serial.begin(115200);           // Initialize serial communications with the PC
  Wire.begin();                   // Initialize I2C
  
  mfrc522.PCD_Init();             // Init MFRC522
  ShowReaderDetails();            // Show details of PCD - MFRC522 Card Reader details
  Serial.println(F("Scan PICC to see UID, type, and data blocks..."));
  M5.Lcd.println("Scan PICC to see UID, type, and data blocks...");
}

void loop() {
  // Look for new cards, and select one if present
  if ( ! mfrc522.PICC_IsNewCardPresent() || ! mfrc522.PICC_ReadCardSerial() ) {
    delay(50);
    return;
  }
  
  // Now a card is selected. The UID and SAK is in mfrc522.uid.
  
  // Dump UID
  Serial.print(F("Card UID:"));
  M5.Lcd.println(" ");
  for (byte i = 0; i < mfrc522.uid.size; i++) {
    Serial.print(mfrc522.uid.uidByte[i] < 0x10 ? " 0" : " ");
    Serial.print(mfrc522.uid.uidByte[i], HEX);
    M5.Lcd.print(mfrc522.uid.uidByte[i] < 0x10 ? " 0" : " ");
    M5.Lcd.print(mfrc522.uid.uidByte[i], HEX);
  } 
  Serial.println();
  
}

void ShowReaderDetails() {
  // Get the MFRC522 software version
  byte v = mfrc522.PCD_ReadRegister(mfrc522.VersionReg);
  Serial.print(F("MFRC522 Software Version: 0x"));
  Serial.print(v, HEX);
  if (v == 0x91)
    Serial.print(F(" = v1.0"));
  else if (v == 0x92)
    Serial.print(F(" = v2.0"));
  else
    Serial.print(F(" (unknown)"));
  Serial.println("");
  // When 0x00 or 0xFF is returned, communication probably failed
  if ((v == 0x00) || (v == 0xFF)) {
    Serial.println(F("WARNING: Communication failure, is the MFRC522 properly connected?"));
  }
}

obviously the esp camera does not have an lcd, so you would delete those lines and keep the serial lines.

Where can I check the camera version?
Software firmware version?

My camera is model B in this photo.