Not sure if you're seeing something different on that page, but for my view, the "widget" page makes no mention of "wedjat" and vice versa. But it is spelled "wadjet" instead .. and that page makes no mention of widget either.

Etymology 1 Coined by George S. Kaufman in his play Beggar on Horseback (1924).

Edit: that wedjat/wadjet does not appear on the page does alone suggest there's no link.

Not necessary (rgd the edit). Comparative linguistics (however questionable) is a thing. For example, the page for October - https://en.wiktionary.org/wiki/October - does not mention any connection to indo-germanic languages where "october, november and december" have roots that map to the sanskrit "ashta, nava, dasha" (eight, nine, ten) which correspond to the eighth, ninth and tenth months in the roman calendar.

It was coined in 1924. It was made up. Invented. Which part of that was unclear?

For some reason that didn't hit me at all. Perhaps I was already in a mode to draw a link. Apologies.

No problem, we've all done that.