The poskim bring down that we should overflow our cups of wine for havdalah and this is a good siman. The gemara says we should eat certain foods on rosh hashana and they are simina milsa? What does that mean? Are we saying that this act should bring us hatzlacha in the future?
The Ben Ish Chai addresses this question with regard to the custom of opening one’s hand upon reciting the words “pote’ach es yadecha u-masbia le-chol chai ratzon.” He explains that the idea of opening one’s hand is to make a “concrete action that corresponds to the spiritual receiving of influence (shefa)” (Shana 1, Vayigash 12).
A similar idea is expressed by the Damesek Eliezer (9:1), and an earlier source for the concept can be found in the Ramban.
It appears that this is also the idea behind the overflowing cup of wine on Motzaei Shabbos.
The blessing of Shabbos overflows, in a spiritual sense, into the week: Shabbos is a source of blessing, and although on the one hand Shabbos is the climax of the week, it also serves as a source of blessing with which the week opens. Thus, the concept of Tosefes Shabbos brings the holiness of Shabbos into Sunday, and the week begins with the Kedusha of Shabbos.
This spiritual idea is given a physical representation and manifestation in the overflowing of our cup of wine. The wine of havdallah, which is the final mitzvah of Shabbos, overflows, suggesting the overflowing of the holiness of Shabbos into the weekdays. As the Ben Ish Chai writes,
It is a good custom to give the spiritual a tangible expression here, and presumably it serves to make the effect real and part of our lives.
It would appear that this is the simple explanation even for the simanim of Rosh Hashanah, together with the opportunity to add prayers and requests for the blessings of the new year.
Best wishes as always.