Korbanot of Rosh Chodesh on R"H
During p'sukei d'zimra on a week day which is Rosh Chodesh, we add in, during the recitation of Korbanot, a paragraph about the sacrifices of Rosh Chodesh.
On Shabbat, add in an extra paragraph with the korbanot of Shabbat.
But on Rosh Hashana, we don't add in the korbanot of Rosh Chodesh even though the first day of Rosh Hashana is Rosh Chodesh. In fact, according to the chart on this page, the korbanot of Rosh Chodesh are given on Rosh Hashana (I assume, the first day) so if we give them on that day, and saying korbanot helps take their place, we are missing out by not adding them in at the beginning of davening.
The chabad website gives an answer that posits that the rabbis didn't want people to be confused because only the first day is Rosh Chodesh and people might mistakenly say the R"C prayers on the second day as well. But there are plenty of prayers which we only say on one day of Rosh Hashana and not the other. If it is Shabbat on the first day,w e add in the korbanot of Shabbat (at least according to the Artscroll Machzor). So why wouldn't we add in the Rosh Chodesh korbanot in P'sukei D'Zimra?