Does Trent’s Canon 5 on Baptism refer to the Sacrament? Yes.

Yes, Pope Paul III does refer to water baptism in that quote.  We’ve mentioned this before, but some people don’t seem pay attention to the point.  The above canon is a canon on the Sacrament of Baptism (Canones de sacramento baptismi).  We repeat: it’s a canon on the Sacrament of Baptism.  The so-called “baptism of desire” is not, even according to those who believe in it, a sacrament:

Fr. Laisney, Is Feeneyism Catholic?, baptism of desire advocate, p. 9: “Baptism of Desire is not a sacrament; it does not have the exterior sign required in the sacraments.  The theologians, following St. Thomas… call it ‘baptism’ only because it produces the grace of baptism… yet it does not produce the sacramental character.”

Since only water baptism is the sacrament, Pope Paul III does define that water baptism is necessary for salvation without exception by defining that the sacrament is necessary for salvation without exception.  This refutes what you stated above. To your second point, that the Catholic Church has allowed other forms of baptism, that is simply not true.  Certain men have fallibly theorized such, but the Catholic Church hasn’t taught it.  In fact, your statement that there are other forms of baptism contradicts the defined teaching of the Catholic Church that there is only one form of baptism, which is celebrated in water.

Pope Clement V, Council of Vienne, 1311-1312, ex cathedra:  “Besides, one baptism which regenerates all who are baptized in Christ must be faithfully confessed by all just as ‘one God and one faith’ [Eph. 4:5], which celebrated in waterin the name of the Father and of the Son and of the Holy Spirit we believe to be commonly the perfect remedy for salvation for adults as for children.”