the Chazzan announces (during Rosh Chodesh Bentching)
the day Rosh Chodesh will be on, similar to the times when they
were Mekadesh the Chodesh.
R. Akiva Eiger zt"l , writes on himself “בער אנכי"
(I am an AmHa’aretz)* and I don’t know where do we find קידוש החדש
was done standing. From the Mishna (R.H. 25b) it seems the
opposite, Bais Din was sitting, only the עדים were standing.”
(Bais Din announced מקודש while they sat)
I once heard an answer . In Pirkei D’rabi Eliezer it says
a Sefer Torah was brought in when the Bais Din said מקודש-.
When a Sefer Torah is brought in, everybody needs to stand up.
Our Minhag is, for the Chazzan to hold the Sefer Torah during
time he announces the new Chodesh. Perhaps it is done lezecher the
קידוש החדש where they brought in a Sefer Torah.
According to the Mishna Verura, (Shar Hatzion 146 sk18) there is no
חיוב to stand while the Chazan is standing and holding the
(Rosh Chodesh Bentchen, Eil Molei, Mi Shebeirach Bahab etc.)
The Minhag is to stand because of הידור תורה .
The only time you must stand, is while the Chazzan walks
with the Torah or for Hagbah.
*We should all be an Am Ha'aretz like him.