Does merely reading horoscopes—while believing in their falsehood and that knowledge of the unseen rests with Allah—fall under the category of shirk, and does it invalidate prayers for 40 days because of that?

What you did by looking into horoscopes is not disbelief (kufr), but it is forbidden (haram). It requires sincere repentance (tawbah nasuh) by which the threat of punishment is removed. With repentance, the prayer will be accepted, and repentance erases sin, for the Prophet, peace and blessings be upon him, said: "The one who repents from sin is like one who has no sin."