Is worship during the end of the year, such as prayer, reading the Qur'an, or Dhikr, which is promoted by circulating messages, considered a reprehensible innovation (bid'ah munkarah)?

There is no harm in sending messages via various communication channels to encourage prayer (Salat) and remembrance (Dhikr). This falls under enjoining what is good and cooperating in righteousness and piety. Allocating this to a time when people are heedless and sins are widespread is legislated, because warning against sins becomes more emphasized when they are prevalent. However, these messages must be free of any Sharia violations.