Please, for G-d's sake do not even think putting cabbage into Solyanka, big-big no-no. Also just like I am a big defender of the fact that Borscht is Ukrainian, the solyanka by the same token is absolutely Russian. The name "solyanka" has nothing to do with salt either, even though it does sound like Russian word for salt, in fact "solyanka" in this case comes from old Russian and means something that was put/assembled together, in this case bunch of different cold cuts, leftovers of different meats.
P.S. Even the picture is wrong. In the original recipe there are no carrots, or parsley/parsnip. That is why I suggest in my recipe to grate it so by the time you are done cooking you do not see them. I simply like my soups very thick. You can add celery, but I have to tell you the truth, in my 29 years of living in that country not only I have not seen celery, I never heard about it. Neither does it need bay leaves, sound to me like they are mixing two different soups together, or even 3.