Opera means "works," and it has meant that for a very long time.
Etymonline says English took the word in the 1640s from Italian, where it meant "a work, labor, composition." The Italian came from Latin opera, "work, effort." That Latin word was originally the plural of opus, "a work," but Latin speakers treated it as a feminine singular. So the grammatical shift people blame on Italian happened earlier, in Latin itself.
The root goes back to the Proto-Indo-European op-, "to work, produce in abundance."
The music came first and the name followed. Wikipedia says Jacopo Peri's Dafne, written around 1597, is regarded as the earliest work that counts as opera, though not all authorities agree. Citing the OED, it dates the Italian word for the genre to 1639, so for over forty years the art form had no settled name. The first English use in that sense is dated to 1648, which fits Etymonline's 1640s.
Etymonline quotes Elson's Music Dictionary on the beginnings of the form. It arose shortly before 1600, when Florentine enthusiasts tried to bring back Greek plays to the modern stage.
English then built a small vocabulary around it:
- opera-house in 1720
- opera glass, small binoculars for the theater, in 1738
- operatic in 1749
- opus in 1809, the Latin singular, borrowed after the plural had settled in
That last item is the tidy joke. English took the plural opera first and the singular opus second. Etymonline also lists French oeuvre as a doublet of opera, meaning both words come from the same Latin source by different routes.
The family is large. Etymonline's entry for the root op- lists office, optimism, opulent and cooperate as words that may be descended from it.