This is new feature and I didn't find API for that in RTD or in HSE DEMO examples. So, I used minimalist option and I simply triggered the service via MU in debugger. Here is the description of the service from API manual:
c:\NXP\HSE_FW_S32K312_0_2_40_0\docs\S32K312_HSE_Service_API_Reference_Manual.pdf


So, the service ID is 0x57 and no parameters are needed.
Just write 0x57 somewhere to RAM and then write address of this RAM word to Message Unit MU_0, register TR[1]. That's all. Then you will see the response in RR[1]. If the HSE FW was installed, you should get HSE_SRV_RSP_OK which is value 0x55A5AA33.
Here's how it looks in my debugger:
