The hardware SPI is not the best for these sorts of devices, as it is limited to 8 bit transfers at a time.
The SSI protocol is similar but supports an arbitrary number of bits in one transfer, and is usually implemented in software.
The Microwire library does that for you: GitHub - tim0s/MicrowireEEPROM: Read and write EEPROMs using the Microwire protocol, such as the ST93C66
Have you googled to see if someone has already interfaced this sensor with Arduino? I have seen Arduino used with other SSI magnetic encoders. Google "arduino ssi encoder" for examples, e.g. AS5600 Magnetic Rotary Position Sensor - Setup - #7 by kundun