Earlier quoted context omitted.
Yeah, it's 'borsjtsj'. No idea why. Presumably it's the closest approximation of that phoneme in Dutch, but it seems unlikely that anyone trying to pronounce the Dutch transliteration would get anywhere close to the Russian original. Borsjt or possibly even borsj would probably be better.
There is good reason for the Dutch transliteration. Compare English, where /ʃ/ is a very common phoneme, but due to deriving the alphabet from Latin (which had no /ʃ/), there is no letter for it. People are taught that the sound is spelled "sh", but that's not quite true: mission contrition sure And as all of those examples illustrate, in addition to being a phoneme in its own right, [ʃ] is also the English allophoni…
My uneducated guess on /ʒ/ is that /dʒ/ is the most common way of encountering it, so people aren't comfortable separating it out, even though it's still common. It probably doesn't help that the usual transcription is zh which basically doesn't exist in native English words.