Thank you Felix, I solved my problem, it was clearly an internal pullup detail:

  esp_sleep_enable_ext0_wakeup(GPIO_NUM_37,0);//Configure GPIO37 as ext0 wake up source for low logic level
  gpio_pullup_en(GPIO_NUM_37);

Hello everyone,
I am can successfully put my StickC to light sleep using a timer, but I would like to be able to wake it up either using the timer (on its own), or by pressing the A button.
This is the code I'm using:

#define BUTTON_PIN_BITMASK 0x2000000000 // 2^37 in hex

  esp_sleep_enable_timer_wakeup(TIME_TO_SLEEP * uS_TO_S_FACTOR);
  esp_sleep_enable_ext1_wakeup(BUTTON_PIN_BITMASK,ESP_EXT1_WAKEUP_ANY_HIGH); //wake up when Button A is pressed
  Serial.println("Setup ESP32 to sleep for every " + String(TIME_TO_SLEEP) +
  " Seconds");
  esp_light_sleep_start();

This is the guide I used: https://randomnerdtutorials.com/esp32-external-wake-up-deep-sleep/

My guess is that it's got something to do with the PIN 37 being interlanny pulled up or down, but I'm stuck now...
What do you think?

Thank you all in advance!

@jmakiv I am curious about this as well. I got the module and my sim card from Deutsche Telekom should arrive tomorrow.