Is it permissible to work in a bakery that sells cakes for the New Year and sweets for weddings, which may lead to me helping in sin and transgression?.
There is nothing wrong with distributing sweets and gifts at weddings and other happy occasions.
It is still customary in Muslim countries, and no one objects to it. See the answer the question no. 134163
With regard to cakes for the New Year, it is not permissible to help with making them or selling them, because that is helping in sin and transgression, because the New Year is not one of the Muslim festivals, so it is not permissible to celebrate it or to help those who celebrate it.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
Congratulating the kuffaar on the occasion of Christmas or any of their other religious festivals is haraam according to consensus, because that involves approving of what they follow of symbols of kufr and approving that for them, even if he does not approve of this kufr for himself, as it is haraam for the Muslim to approve of the symbols of kufr or to congratulate someone else for them. Similarly it is haraam for the Muslims to imitate the kuffaar by holding celebrations on that occasion or exchanging gifts or distributing sweets or plates of food, or taking time off work and so on, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever imitates a people is one of them.” Narrated by Abu Dawood, 4301.
Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen, 3/45-46
And Allah knows best.