“Sprinkling” is the internalized metaphorical sprinkling of the Last Supper and of the Eucharistic Sacrifice. The author “kaleidoscoped” the 2 respective covenantal sprinklings already in Heb 9:18-20, and since the book of the old Law was said by him to have been “sprinkled” even though Ex 24:6-11 never says it was, he means the new Law, now being in this new covenant “within you” (instead of in the form of a book external to you as in the first covenant)is “sprinkled” by the “poured out” blood (“aimatochysia” Heb 9:22) that was drunk at The Last Supper in the present tense on that occasion (see strict Gr philology for a Eucharistic-realist exegesis of the Last Supper institution accounts).
Thus mediator of covenant and blood poured out (sprinkled) are paired at 12:24 since mediator of NC and HP according to Melchizedek are the two dominant thematic roles for Jesus in Hebrews.
The author knew of the tradition that said the sacrifices of Cain and Abel were offered 14th of Nisan. Given the Zion/Sinai parallelism theme here, we note Jesus offered, like Moses “the Pasch and ‘the sprinkling’ “ both (Heb 11:28), they were offered on 14 Nisan, they were (the Supper that is) on Mt. Zion, and they were the “blood that spoke” (Heb 12:25, Gen 4:10).
In the law of Moses, blood spoke — had its own voice — and sacrificially-offered blood had its own particular significance. The blood “of sprinkling” indicates conformity to a public cultic rite, and the idea that it speaks means a strict comparison — NOT TO ABEL’S SLAIN BLOOD — but rather to the sacrificial blood Abel pleasingly and creditably offered to God.
Finally 12:24 says the believer has come to this sprinkling. Why not, since it is offered “from the earth” (Gen 4:10, Is 42:10, Ps 148:7, Ps 8:1, Ps 56:5-7, Mal 1:11).