SCX-3400 Series Printer Works with the SCX-3200 Driver
The Samsung SCX-3400 Series Printer Works with the SCX-3200 Driver
Recording this somewhere so others may find it.
Available printer drivers (now from HP) for SCX-3200 and SCX-3400 series models appear to be for old Mac operating system versions.
However, it may be of some interest that at least the following exact models are listed as supported in About AirPrint - Apple Support (en-us edition February 12, 2025):
Samsung SCX-3205W
Samsung SCX-3205WK
Samsung SCX-3206W
Samsung SCX-3405FW
Samsung SCX-3405HW
Samsung SCX-3405W
Samsung SCX-3406FW
Samsung SCX-3406HW
Samsung SCX-3406W
Samsung SCX-3407W
An AirPrint-enabled printer can be used without additional drivers even on a more modern Mac, and without an extra app on an iPhone or iPad. This provided that the printer and the Mac/iPhone/iPad are connected to the same network (Wi-Fi router).