"METONYMY" is not an alternate to reality. It does not mean mere shadow and type. It is simply the extension of one term to include a related aspect of the same entity. To say something is called something "by metonymy" doesn't brush it away as a fact. The dictionary definition of "metonymy" is:
"The use of the name of one thing for that of another of which it is an attribute, or with which it is associated."
Sin, literally and primarily, is transgression of God's law. That is the root meaning, from which others flow. The term "sin" is scripturally extended by the process called "metonymy" (extending a name to include a related thing) to include the evil, corrupt, death-bringing principle in every cell and particle of human flesh - the diabolos - that causes all diseases and death and disharmony with God: and which normally (unless there is direct Divine interference, as in the unique case of Christ) will inevitably bring forth its fruits of actual transgression.
This evil principle in the flesh is both the result of sin, and the cause of sin, and therefore the Scriptures go to the root of the matter, and give the name "sin" to it (just as they call hate, "murder"; and lust, "adultery") - and they deal with all sin as an inseparable totality.
Actual transgression, and the evil principle that Paul calls "the Law of Sin in the members," (or "Sin in the flesh," or the diabolos) - are inseparable parts of the total sin constitution that Christ came to destroy and abolish. Therefore the Scriptures, which deal with roots and realities, and not mere superficial appearances, gives the same name to all: SIN.
"Metonymy" is not a magic word to change a Yes to a No, or a fact into not a fact. It is simply a description of a process, illustrated in this case by the Scriptures grouping together everything to do with sin under the name Sin.
When you see "metonymy," just remember "another name" - that's what it means - and in this case, a scriptural, God-given name.
To say it is "metonymy," doesn't change the fact that God (the Supreme and All-Wise Authority) gave the name "SIN" to the evil principle in all human flesh.