I recognize that this is a serious question.
With all due respect, the first thing to note is that the Internet provides only a funhouse-mirror distortion of Catholicism--- simply because it is a funhouse distortion of everything, making noses huge and chins tiny, elongating fingers and shrinking legs (you get the picture).
It's like comparing Mozart to Miley Cyrus in number of google searches. Yow. Can't use that as a criterion of what's significant and what's not.
For an undistorted view, it's better to look at how we actually pray, e.g. liturgical prayer. Just for starters, the Mass prayers (this is what we pray every day) and the Scripture readings from last Sunday's Mass (this runs through the Bible on a 3-year cycle of daily readings.)
Use your search function to make it quick-- Mary was not even mentioned in last Sunday's readings, and is mentioned zero times in an ordinary daily Mass.
You may have noticed that there are two places where she is mentioned --- and that, briefly --- in a Sunday Mass: in the Confiteor and the Nicene Creed. In the Confiteor, Mary, exactly like all of US, the "brothers and sisters," is asked to pray to God for us. Just --- as I said --- the same way we ask each other to pray to God.
In the Creed, we acknowledge that Christ was "born of the Virgin Mary."
That's it.
I hope you can see that this is a more proportionate view than what you may find at myriad internet site.
Then how “orthodox” is the Rosary considered in Catholicism?
Mary is mentioned almost constantly in that recitation.