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!

Hrm. I haven't even heard that so far, maybe because I rarely did meetings.

Looking it up in https://en.wikipedia.org/wiki/Segue they even warn about that!