That said, if you ask Orthodox Jews, they will say it's not circumventing the laws about shabbat. Rather, it's keeping the laws of shabbat -- avoiding all forms of work -- while still living in the modern world. To circumvent the law would be to find a way that allows us to work on shabbat. Shabbat mode doesn't do that.
https://en.wikipedia.org/wiki/Talmud#Pilpul
In that aspect, Judaism is very different from, say, Christianity.
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Me too. When someone asked me whether such-and-so was work, I would have just said, "Use your judgment. If it feels like work, it's work."
And the reason for that is that it's not about work, but about creative action.
Whether operating electric lights is work is a new problem, but boiling water and cooking have been forbidden by Jewish law for at least 2,000 years.
That's because work is not the correct translation. A better translation is "creative activity", i.e. creating things, like light.
God stopped creating the world on the Sabbath, so Jews also stop creating things (and there is a specific list of what is included).