Laws of Shiva when the deceased passed away on the eve of a holiday and Shiva was not observed

If one's father passed away and was buried on the eve of Shavuot, and the mourning rites were not observed before the holiday, what are the laws regarding Shiva and Shloshim?

Since Shiva was not observed before the holiday, Shiva and Shloshim are not canceled. Therefore, Shiva must be observed after the holiday. From the thirty days, an additional 22 days must be completed because the holiday is considered as seven days, even though Shiva was not observed before it.

It is stated in the Gemara Moed Katan, page 24, side 2: "Rabbi Anani bar Shashon taught at the entrance of the house of the Nasi: one day before Shavuot and Shavuot itself count as fourteen days." This is also ruled in the Shulchan Aruch, Siman 399, paragraph 8. This applies when mourning customs were observed before Shavuot, but if mourning customs were not observed before Shavuot, the days between Shavuot are not considered as seven, but Shavuot itself is considered as seven.
This is also written by Tiferet Le-Moshe, Yoreh De'ah, Siman 399: "In Shulchan Aruch, Siman 399, paragraph 1, it is written: 'But if he erred or intentionally did not observe mourning, etc.' However, it seems that in such a case, Rosh Hashanah and Shavuot are considered as seven days, and this explains why the commentators were puzzled by what is said in the tractate 'Eilu Megalchin': one day before Rosh Hashanah and Rosh Hashanah itself count as fourteen days. What is the significance of this? Since Yom Kippur cancels the decree of thirty days. See in Tosafot, page 24, side 2, that it matters if they buried seven days before Rosh Hashanah and did not observe mourning until two days after Yom Kippur, then there is no need to complete, as it is considered as if thirty days have passed, as stated in Siman 396, that completion is only possible within thirty days.
Thus, if buried seven days before Rosh Hashanah, the thirty days end two days after Yom Kippur, as the seven days from burial to Rosh Hashanah, and another two days of Rosh Hashanah are considered as seven, totaling 14, and another seven days between Rosh Hashanah and Yom Kippur, totaling 21. Yom Kippur itself is considered as seven, totaling 28, and another two days after it, totaling thirty. This proves that the days before the holiday are counted as their number since mourning was not observed, but the days of the holiday are always considered as seven.