Hi Leo,
I trying this project again and setup clock follow your screenshot but still is there HARDFAULT.
One question: you r screenshot is from what environment-versions? MCU, S32DS.RTD? Because main looks different:

and you can see that EMIOS IP is driving from CORE_CLK.
I try to add Emios_Mcl_Ip_Init function (I not sure if that really missing) to my main.c:

and here is exact place where code first time try access EMIOS-MCR register and step over this cause HARDFAULT immediately:

Please can you try my projects on your side?
I again attaching original example which works on FIRC clocks(original_example.zip) and adjusted project(adjusted.zip) witch is switched to ExtOSC 16MHz on my S32K388EVB-Q289 board