Let's say someone gets married and during that person's Sheva Brachos week there is a Fast day that was supposed to be on Shabbos but was pushed off to Sunday. They are within Sheva Brachos on that Sunday. Does their personal Holiday trump the pushed-off fast day, or does the fast day win out? Does it make a difference which fast day it is? (Of course CYLOR)
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The Aruch HaShulchan writes in OH 559:9 that although from the letter of the law, when Tisha b'Av is pushed off from Shabbos, people involved in a bris can daven mincha and then break the fast during the day, that "we never heard of anyone doing such a thing" and that not only for Tisha b'Av, but on any fast that is pushed off, we don't make any meal during the day for any simcha, not a bris nor a pidyon haben, and thus is the minhag and one should not change it.
Although see R. Ovadia in Yechave Daas 3:37 who addresses precisely the question of newlyweds during sheva brachos and concludes leniently that they need not complete the fast.
The only Biur Halacha to OC 549 strongly implies that the bride and groom do not need to complete the fast when it is pushed off, but they do when it is not pushed off. He implies that all 4 of the Churban-related fasts are the same in this regard. (Rav Ovadia Yosef makes a parallel diyuk to what I am making in Yehavveh Da'at 3:37).
While the Magen Avraham (OC 559 sk 11) rules that the bride and groom only break the fast on the first of the seven days, the Mishna Berurah questions this conclusion in Shaar HaTziyun 559 sk 34.
This Mishna Berurah is relied upon lemaaseh for the fast this year by Rabbi Aryeh Lebowitz in this recorded shiur.
Ps It is funny as @doubledd said in comment above but it is possible that the bride will still need to fast