"You shall not eat anything with the blood, nor practice divination or soothsaying." (Leviticus 19:26)
"There shall not be found among you anyone who makes his son or his daughter pass through the fire, one who uses divination, one who practices witchcraft, or one who interprets omens, or a sorcerer, or one who casts a spell, or a medium, or a spiritist, or one who calls up the dead." (Deuteronomy 18:10-11)
"And when they say to you, “Inquire of the mediums and the necromancers who chirp and mutter,” should not a people inquire of their God? Should they inquire of the dead on behalf of the living? To the teaching and to the testimony! If they will not speak according to this word, it is because they have no dawn." (Isaiah 8:19-20)
Why even try contacting dead people if their souls are not consciously existing? Certainly, the Jews would have known that the souls of the deceased were no longer aware of anything at all. Such efforts at communication would have already been known to be guaranteed failures (not that it works anyway). So it is obvious that biblical prohibitions against contacting the dead presuppose conscious life after death. If soul sleep is true, then such commandments from God would be meaningless.
In addition, such a teaching (no conscious life after physical death) violates the clear witness of Scripture:
"Nevertheless I am continually with You; You have taken hold of my right hand. With Your counsel You will guide me, and afterward receive me to glory. Whom have I in heaven but You? And besides You, I desire nothing on earth. My flesh and my heart may fail, but God is the strength of my heart and my portion forever." (Psalm 73:23-26)
"For as the body apart from the spirit is dead, so also faith apart from works is dead." (James 2:26)
"I consider it right, as long as I am in this earthly dwelling, to stir you up by way of reminder, knowing that the laying aside of my earthly dwelling is imminent, as also our Lord Jesus Christ has made clear to me." (2 Peter 1:13-14)