Shadal, while commenting on the word זמרת in Exodus 15:2, discusses cases where there is a kamats instead of the expected patach (or other reduction) in smikhut. The cases he mentions are:
Isaiah 11:11 "שאָר עמו", Isaiah 45:13 "גָלותי" Esther 1:4 "יקָר תפארת גדולתו", Esther 1:20 "פתגָם המלך", Esther 4:8 "כתָב הדת", Job 34:25 "מעבָדיהם", II Chronicles 31:3 "מנָת המלך".
He says about these (translation by Daniel Klein, from Shadal on Exodus):
... the word does indeed preserve a kamats, but that kamats is
aramaic (as in the Syriac מְנָתָא...), not a Hebrew kamats...
Because it is an archaic kamats, it does not change [to a pataḩ].
Although it is noteworthy that Shadal does not list your explicit examples (even though he lists several other examples from Esther), he might extend the same explanation to those as well, viz. that these kamatses are archaic holdovers from an earlier Hebrew, comparable to one preserved in Aramaic.
In his grammatical treatise Prolegomena to a Grammar of the Hebrew Language, Shadal speaks further on this phenomenon of an "immutable Aramaic kamats". He says (in Section 138, translated by Aaron Rubin):
In the passage of Aramaic words into Hebrew, the Aramaic קמץ, where it does not change to וֹ (see Section 126a [where, for example, the phenomenon of שְלָם to שָלוֹם is described]), normally preserves its immutability, though not with the same constancy as in Aramaic.
He lists examples, which again notably does not include דָת. He then (in Section 140) lists examples where the kamats became mutable, again not listing our example דָת.
Thus, although it is impossible to make a definitive conclusion from Shadal about דָת, since it is conspicuously absent from both sides of the discussion, one could argue (especially based on the evidence in our text of Tanakh) that he would include the kamats in דָת among the immutable kamats (of which his list includes the words "for example"), and thus carrying over to the construct form and plural. If this is indeed the case, then ArtScroll is incorrect1, and the correct pointing would always be with a kamats2.
1 On the other hand, the exact language of הרי את does not seem to be a required part of kiddushin. Thus, any language that implies kiddushin is acceptable. Since דַת with a patach is correct in modern Hebrew (according to Even Shoshan), it might not be incorrect to use modern Hebrew, and hence this formulation, nowadays in effecting kiddushin.
2 We can see from the Prolegomena that Shadal posits correct pronunciation based on his discussion for words in common parlance (like שְׁטָרֵי and כְּתָבֵי), not just Biblical pointing.