I updated @auct's code to include the built in button as well:

#include <Adafruit_NeoPixel.h>

#define BUTTON_PIN 3
#define PIXEL_PIN 2
#define NUM_PIXELS 1

Adafruit_NeoPixel pixel(NUM_PIXELS, PIXEL_PIN, NEO_GRBW + NEO_KHZ400);
bool currentButtonPressed = false;

void setup()
{
   // set up serial out
  Serial.begin(115200);

  // set up neopixel
  pixel.begin(); // INITIALIZE NeoPixel strip object (REQUIRED)
  pixel.clear(); // Set pixel colors to 'off'
  pixel.show();
  
  // set up GPIO
  pinMode(BUTTON_PIN, INPUT_PULLUP);

  // initial button pressed state
  setPixelToCurrentButtonState();
}

void loop()
{
  // read button state (LOW when pressed)
  bool newButtonPressed = digitalRead(BUTTON_PIN) == LOW;
  setPixelStateIfChanged(newButtonPressed);

  delay(10); // debounce
}

void setPixelStateIfChanged(bool newButtonPressed) {
  if (newButtonPressed != currentButtonPressed) {
    currentButtonPressed = newButtonPressed;
    setPixelToCurrentButtonState();
  }
}

void setPixelToCurrentButtonState() {
  if (currentButtonPressed) {
    Serial.println("turning LED blue");
    pixel.setPixelColor(0, pixel.Color(0, 0, 128));
    pixel.show(); 
  } else {
    Serial.println("turning LED red");
    pixel.setPixelColor(0, pixel.Color(128, 0, 0));
    pixel.show(); 
  }
}

I updated @auct's code to include the built in button as well:

#include <Adafruit_NeoPixel.h>

#define BUTTON_PIN 3
#define PIXEL_PIN 2
#define NUM_PIXELS 1

Adafruit_NeoPixel pixel(NUM_PIXELS, PIXEL_PIN, NEO_GRBW + NEO_KHZ400);
bool currentButtonPressed = false;

void setup()
{
   // set up serial out
  Serial.begin(115200);

  // set up neopixel
  pixel.begin(); // INITIALIZE NeoPixel strip object (REQUIRED)
  pixel.clear(); // Set pixel colors to 'off'
  pixel.show();
  
  // set up GPIO
  pinMode(BUTTON_PIN, INPUT_PULLUP);

  // initial button pressed state
  setPixelToCurrentButtonState();
}

void loop()
{
  // read button state (LOW when pressed)
  bool newButtonPressed = digitalRead(BUTTON_PIN) == LOW;
  setPixelStateIfChanged(newButtonPressed);

  delay(10); // debounce
}

void setPixelStateIfChanged(bool newButtonPressed) {
  if (newButtonPressed != currentButtonPressed) {
    currentButtonPressed = newButtonPressed;
    setPixelToCurrentButtonState();
  }
}

void setPixelToCurrentButtonState() {
  if (currentButtonPressed) {
    Serial.println("turning LED blue");
    pixel.setPixelColor(0, pixel.Color(0, 0, 128));
    pixel.show(); 
  } else {
    Serial.println("turning LED red");
    pixel.setPixelColor(0, pixel.Color(128, 0, 0));
    pixel.show(); 
  }
}

@auct Thank you! After adding the Adafruit neopixel library to the arduino IDE, this worked great!

I'll also note that I had issues flashing code to the C3 with my Mac (running OSX Catalina with updated drivers) but using a Windows machine fixed that issue.

These examples would be very much appreciated. I've been having trouble getting ESP-IDF or Arduino IDE to flash any code to my M5Stamp-C3 since there are virtually no examples of how to do this on the internet.