Then how “orthodox” is the Rosary considered in Catholicism?
Mary is mentioned almost constantly in that recitation.
Actually only two mysteries are about Mary
Let’s take a look
Joyful Mysteries — Conception, birth and childhood of Jesus Christ
Luminous Mysteries — the Adult Ministry of Jesus Christ from his Baptism to the Last Supper
Sorrowful Mysteries — from the Agony in the Garden to the Crucifixion
Glorious Mysteries — first three — Resurrection, Ascension, Descent of the Holy Spirit, then the two about Mary
So you see the Rosary is really about Christ.
While we say it we meditate on these incidents in his life.