FWIW, I did a quick search of our local slack and found 2x the the number of instances of "segue" compared to "segway". And most of the instances of "segway" (around 60%) refer to the actual device, with only a handful of mistakes (around 4). So I'm not sure that this spelling is more common in a corporate environment—maybe do a search for yourself and see!
A recent phenomenon that I am seeing on LI is that these so called LinkedIn top voices take some random tiktok kind of videos, and then wrap some generic management spiel around it to give what we call here in India as "gyan", or, sharing their supposedly vast management knowledge with their followers. Totally hollow and cring-worthy.
Yet, there is sometime some good content. So, like with everything else, take what works for you, ignore, what does not.