…in the meantime I got a reply from Dragino support:
The solution is to flash the device with a different frequency image which will do a factory reset and also reset the password to its default.
After flashing again with the correct frequency image the device works as before and AT commands can be issued again as expected 
For flashing I used the STM32CubeProgrammer.
The recommended STM32 Flash loader demonstrator (FLASHER-STM32) did not work for me.
BTW, I have no idea why changing the password failed because I only used a very simple and short PW.
But now I really don’t think it’s necessary to change it and will keep the standard for the time being 
Best regards,
Stefan