S32K3 RTD 4.0.0 is compatible with S32K344.
Which S32 Configuration Tool did you choose? Pins tool or Clocks tool or Peripherals tool? The other tools should not support S32K344.

If it is not the above problem, maybe some dependent software packages are missing during installation. It is recommended to refer to this post for offline installation: HOWTO: offline install S32K3 RTD 3.0.0 in S32DS v3.5
The following are the differences between installing S32K3 RTD3.0.0 and RTD 4.0.0:
Unchecking Contact all update sites during install to find required software can complete offline installation faster. (When you confirm that you only need to install these selected software)
Step2. S32 Design Studio 3.5 Update 8 D2311: SW32_S32DS_3.5.8_D2311.zip
Step3. Download and Install S32 Design Studio 3.5.8 Development Package with support for S32K3xx devices(3.5.8_D2311): SW32K3_S32DS_3.5.8_D2311.zip
Step4. Download and install S32K396 RTD for development, please download and install S32 Design Studio 3.5.6 RTM with support fo...(3.5.6_D2309): SW32K39x_S32DS_3.5.6_D2309.zip
Step5. If you only need S32K3 but not S32M2, you do not need to install the fifth step.
Step6. Download and install S32K3_Real-Time Drivers AUTOSAR R21-11 Version 4.0.0 Patch 16: SW32K3_RTD_R21-11_4.0.0_P16_DS_updatesite_D2404.zip
Need to install S32 Design Studio S32K396 SDK.