Put the chip in deep sleep with all wakeup sources disabled.

Your first code sample is for the Arduino platform and the second is for ESP-IDF. The private wifi.h header in ESP-IDF isn't the same as the WiFi.h header in Arduino and including it won't provide any Arduino-like functionality for your code.

xTaskCreate(&task, "Test Task", 10000, NULL, 1, NULL);


You have extra indirection that causes the code to crash. The call should be:

xTaskCreate(task, "Test Task", 10000, NULL, 1, NULL);

See the example in the docs:
https://docs.espressif.com/projects/esp-idf/en/latest/esp32/api ...

There appears to be a port of Qt for MCUs for the ESP-S3-BOX device: https://doc.qt.io/QtForMCUs-2.3/qtul-supported-platforms.html#other-target-boards . You need to contact the Qt company for access to the code and for setup instructions.
Notice that Qt for MCUs is a small subset of the full Qt ...

Remove the setenv() and tzset() calls from timeSync() function, and place them in setup() before calling getLocalTime().

Try using esp_wifi_set_ps(WIFI_PS_NONE) to disable WiFi power saving mode.

The stack for "Print messages" task is too small and it breaks the other task. In my system, the program crashes after first run of print_messages():
Sending num :: 0
Sent num
Spaces in queue :: 4
Item received :: 0
Guru Meditation Error: Core 0 panic'ed (LoadProhibited). Exception was unhandled ...

Where is the array data_buf allocated? If it's a local variable to the sending function, it won't exist when the message is read and the space may have been overwritten by other data.

The maximum length of a NVS key is 15 characters: https://docs.espressif.com/projects/esp ... and-values, the key "user_msg1_length" you used is 16 characters.

The first comment line of the code states it's an example of the High Resolution Timer API and the documentation for esp_timer_delete() is on that page. No need to guess, just read more carefully.