The firmware is provided in encrypted form as a binary file. Yes, HSE FW installation package contains only the binary (pink) file and corresponding API headers.
For Lauterbach users, there's also HSE DEMOAPP which helps to install the firmware and examine HSE features:

But notice that the demo works with Lauterbach debugger only. It won't work with Pemicro.
As you can read in the mentioned application note or in HSE FW RM, the firmware can be installed with or without IVT.
Installation without IVT is easier but you need a tool which is able to load raw binary file to the flash which is not the case of Pemicro debugger. In this case, "with IVT" method is more convenient.
We do not provide S32K344_HSE_FW_INSTALL for each derivative. This is just an example showing how it can be done and it's up to users to create own solution (each customer has different requirements and production tools/capabilities).
What to do:
You can create new application project directly for S32K312 in S32 Design Studio. Then copy the source files from S32K344_HSE_FW_INSTALL, update HseFwHeader_StartAddress in boot_header.c. Then modify the linker file - use linker file from S32K344_HSE_FW_INSTALL as a template. If you read the readme.md file as I suggested earlier, there must be a link to the bin/pink file, so it is linked to the project.
Then, the code will only enable HSE feature flag by programming any value different from 0xFFFFFFFFFFFFFFFF at address 0x1B000000. Then all the conditions for installation are satisfied - HSE feature flag is enabled, IVT points to valid pink image in flash, so SBAF will install the firmware after next reset.
Regards,
Lukas