The use of beads, similarities in prayer and function, ie the mechanics of the Rosary are based in pagan tradition. No biggie so are a lot of Christian traditions and holidays.
You gotta rule out “covergent evolution.”. Similarity is not sufficient to show shared origin. Both bats and birds have wings.
In any event, other religions practice initiatory “lustrations” and we’re not going to quit doing Baptisms because some pagan also washes.
My studies, FWIW, suggest that knotted string predates beads in Xtian usage, and that first the Rosary was paternosters.
The number of 150 was so that the illiterate could substitute their prayers for the Psalms sung by the “choir monks.”. Of course J2P2’s addition of 5 more mysteries broke the link with the Psalter.
I don’t know when and how the “Mysteries” were added. I do know that they are the heart of the Rosary, while the Ave’s are the flesh, the superficies.
(You do know that the word “bead” seems to be derived from “bede” - bid - pray(er).
I don’t know how far back in Xty knotted string goes. But the Rosary seems to have waited for a millennium to become “popular.”