I could have sworn there was a thread here about this in the past but I can't seem to find it.
The white borscht is called "zurek" or "zhurek". It starts like you say with polish sausage cooked and the water being saved for the base of the soup.
Mysterious things are supposed to be added at this point including a fermented sour bread (don't ask me, I have never been able to get this to work). The fermented bread is called barscz on some websites but I think it is more correctly called zakvas or zur. I think that "barscz" is just the Polish word for borscht but I may not know what I am talking about.
The alternative to fermenting bread at this late hour is to buy a couple of white packets of the flavoring/starter at any Polish deli.
Then we add chunks of mild smoked ham, hard-cooked egg, vinegar and horseradish. Marjoram is a must but if you are using the white packet mix, it already contains marjoram so spice judiciously.
There is another soup called pickle soup that has a mild white creamy base. Red Apple has it sometimes. But that is not the same as what we think of as Easter white borscht.
If you google "zurek" you will be innundated with recipes.
Happy Easter to all! --Joy