thanks a lot for your explanation! Before posting here, I actually did search for a schematic of the green SIM7600 board. With no success. Would be very helpful, to have these schematic too, not only the one of the base board. Maybe even the adding of some capacitor behind the on-board regulator could solve my problem.
I have not only the COM.LTE, but also the GPS module, which draws current from the 3.3v though.
I actually already use an external power supply, added to my custom module. It's a PRM3W-E12-S5, a 5V-output isolated regulator. It's output is connected to the HPWR-Bus. Inside the M5stack-core-basic, I soldered a wire from HPWR to the input fuse.
While this works more or less correctly, I tend to have more problems connecting to the IOT through the SIM module, if this external power supply is used. It's working better, if I use the USB for power supply.
I will try to reverse-engineer the green SIM7600 board, and add a backup capacitor.
Will report back.