Hi Bruce,
When you create the new project and add driver for MKL16Z256, don't use the mdk Manage window to add it, yes, that window really lack driver in the Device, this is the MDK IDE problem.
I highly suggest you add the driver manually, the driver for MKL16Z256 can be downloaded from the nxp official website:
https://mcuxpresso.nxp.com/en/welcome
Just like you have said, choose the processor as MKL16Z256ZXXX, then generate the code and download it.
After you download the official SDK sample code, you can find the MKL16 driver in this folder:

You also can modify the official SDK project, take this project as an example:
SDK_2.2_MKL16Z256xxx4\boards\frdmkl46z\driver_examples\gpio\led_output\mdk
The default example is based on MKL46, so when you open it, you need to change all the MKL46 code to the MKL16 code and driver in folder:
SDK_2.2_MKL16Z256xxx4\devices\MKL16Z4

1. startup_MKL16Z4.s in folder SDK_2.2_MKL16Z256xxx4\devices\MKL16Z4\arm
2. system_MKL16Z4.c and system_MKL16Z4.h in folder SDK_2.2_MKL16Z256xxx4\devices\MKL16Z4
3. project driver should be replaced by the drivers in folder: SDK_2.2_MKL16Z256xxx4\devices\MKL16Z4\drivers
4. modify the options


5, copy MKL16Z256xxx4_flash file from folder SDK_2.2_MKL16Z256xxx4\devices\MKL16Z4\arm to SDK_2.2_MKL16Z256xxx4\boards\frdmkl46z\driver_examples\gpio\led_output\mdk

Then build the project, you can find there no errors.
This is the MKL16 project, I also attach my modified project for your reference.
Wish it helps you!
About the MDK IDE window lack SDK driver problem, you need to contact with MDK IDE side.
If you still have question about it, please kindly let me know.
Have a great day,
Kerry
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