Sleep modes on ESP32S3 and SIM7600 while maintaining MQTT connection

[alhadi]

Hello,

I have an application where I need ESP32S3 to be in light sleep and the cell modem sim7600 to be sleep using DTR pin and "AT+CSCLK=1".
I need the MQTT connection to be up so that when I receive a message on a SUBSCRIBE topic, both will wake up and I can parse the received message.
I'm using esp-modem library on esp-idf v4.4.
The examples provided are too basic for this.
There is an example working with esp light sleep but not cell DTR sleep.

Is there a way to use esp-modem library to have both light sleep and cell sleep working while maintaining MQTT connection?