In Czech Wikipedia, they mention a Czech record from 1957 of 200 words/min. They compare normal writing 20-40 words/min, normal speech 70 words/min, TV speech 80-100 words/min.

So a well-designed modern shorthand could probably go over 200 words/min.

There are still some court reporters in the US using Gregg shorthand, and are able to record at over 200 words per minute. [1]

Modern" shorthand is really largely the same as shorthand as done in the early 20th century though. Gregg and Pitman are both phonetical, so there's really nothing particularly special about modern language that doesn't apply, other than that there may not be brief forms for words such as "cell phone" or "computer", but they could be created, though all it'd do if you don't is slow down your top speed. They're still not ultra-common words though.

[1] https://www.courtreporteredu.org/2015/08/some-federal-court-...

While I do not know about the fastest speed on record, in general, an expert is able to outwrite a fast typist exceeding 150 wpm.