I'm aware that per 'Iqar HaDin (baseline Halakhah), Qitzur Shulhhan 'Arukh - Yalqut Yosef writes that a woman may reveal two finger-breadths of her hair (where her hair connects to her head) while covering her hair.
Nevertheless, I see many women in Israel partially uncovering their hair in the fashion below. Is there an authentic tradition/source for such a covering?
You mean that the head is covered, but the hair hanging down beneath it is visible.
There is some room for discussion about this. The biblical source for hair-covering is the Sotah, and it says "the Kohen shall uncover the woman's head" (not "her hair.")
Rabbi Yehuda Herzl Henkin thus writes in Tradition 37:3:
Nevertheless, R. Feinstein could permit more than a tefah outside the hairline simply by following his own line of reasoning. Since the Torah specifies uncovering the sota’s head and not her hair, the kohen needed to uncover only the hair on the woman’s head, and not what hung down on her neck and shoulders. Consequently, no Torah obligation can be derived for a married woman to cover hair outside her hair- line.
See Rabbi Henkin's article for much more on the subject.
I'm not saying it's permissible, but there is certainly room for discussion about it.
Assuming these aren't falls (i.e. half wigs), they would match up with the way the שלטי גיבורים, a commentary on the Ran, explains hair-covering in Shabbat 64b as I wrote here.
And again in his conclusion:
