~ soy sauce and it definitely doesn't go into the chicken soup
Yes it does :)
Some people might add that to soups after cooking but it isn't a common (or good) ingredient of rosół.
If its celery like, it might be por (leek)
More likely to be pietruszka as Seanus said.
The leaves of pietruszka are flat-leaved parsley, the root (which looks like a parsnip but has a different taste) is called Hamburg Parsley and is not commonly used in English speaking countries but is an everyday ingredient in central and eastern Europe.