Hello @Senspix
I just tried with my SIM7600G (non -H; 3 years old) and M5CoreS3 using aforementioned test program and the modem does react to AT commands just fine after about 14 seconds.
Recently I purchased a separate green board with a SIM7600G-H on it which I use in the same COM.X module. Initially it did not work. Turns out the green board had a layout error - RX and TX needed to be swapped electrically in order to work in the COM.X module.
In conclusion: I can use either SIM7600G or SIM7600G-H with M5CoreS3 just fine.
Thanks
Felix