Liturgy is public worship. Post Vatican II, this became clearer; as pre-conciliar worship seemed mostly devotional for many worshippers.
Public worship of God, from its very beginning, has always used music. Recall the Levites who sang around the Ark.
The Eucharist normally features both times of singing (Hosannah and Gospel Acclamation should ALWAYS be sung, Gloria should usually be sung) AND times of silence like during the post-Communion thanksgiving/meditation.
Properly trained choirs can produce truly magnificent worship, particularly a cappella: the Divine Liturgy does not use instruments, nor are they needed for Gregorian chant.
In typical American parish life the music varies greatly, some places have professionally trained musicians, most have volunteer musicians, some of which are outstanding.
Music can vastly improve worship, or perhaps diminish it when done poorly.
But, for sure, music has been a part of liturgical prayer from its very existence, which was commanded by the LORD.
At the Last Supper Jesus and his apostles sang the traditional psalms of the Passover.
He who sings well prays twice,
Deacon Christopher