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"incumbent settings object" is rather hard to parse, and doesn't in its name indicate what kind of object it is about. Could it be called something like "effective caller" or "effective script context". (I'd probably rename "script settings object" to "script context")
"incumbent" means "currently holding office". "settings object" seems self-explanatory. It's the "settings object currently holding office". This seems accurate. Why is it hard to parse? The problem with "effective" is that it is confusing given the existence of "effective script origin", which I think is a more precise use of the word "effective" (as in, "fulfilling a specified function in fact, though not formally acknowledged as such", in contrast to the "real" origin). The problem with "context" is that we use the term almost 2000 times already, so it's getting a bit overused. "Caller" is ambiguous because there might not be a caller involved. Even "script" is a bit dubious since I expect I'll be starting to use this in other contexts in due course. I agree that the terminology is a bit of a mess, though. I just don't know what would be better.
FWIW, I think 'incumbent' is a great name for this concept, and does a great job of differentiating it from the other possibilities (incumbent script vs entry script). Script Settings is a little weird, but I don't have a great alternative.
I'm closing this give the lack of proposals and the failure of my imagination to come up with any better ones, however, if anyone has a concrete proposal for how to improve these terms, please do reopen the bug.