ST did not publish the register map for this part. Instead they tried to make it easy for you and published an API. Using the API, you need only to write the software layer between the API and your MCU's I2C commands, and you should be ready to roll.
The API functions are a lot easier than poking at registers.
Unfortunately ST's API is a bit large. It's very complete, but it's large.
Both Sparkfun and Polulu wrote a smaller API. Theirs are less complete - but they're small and might do what you need.
My suggestion would be to get the code from ST's web site:
https://www.st.com/content/st_com/en/products/embedded-software/proximity-sensors-software/stsw-img005.html
Give it a try - it should be easy enough.
If you have a really small MCU (or an FPGA), you can also look at the versions from SparkFun or Polulu. (There might be others.)
I always add that if you use their software, send them a few dollars. They're great companies who do awesome work, but they don't make any money off their software.
As you are trying to get an FPGA to work. Look at the SparkFun software. The code they wrote is particularly straight forward.