archipelago

The noun is borrowed from Italian arcipelago (“Aegean Sea; group of many islands”), from arci- (variant of archi- (prefix meaning ‘foremost, primary’)) + pelago (“(open) sea”):

Archi- is derived from Latin archi-, from Ancient Greek ᾰ̓ρχῐ- (ărkhĭ-, prefix denoting primary authority or importance), from ἄρχω (árkhō, “to begin; to lead, rule”) or ᾰ̓ρχός (ărkhós, “leader, ruler”); further etymology uncertain, possibly from Proto-Indo-European *h₂er- (“to fit, put together”) or *h₂ergʰ- (“to begin; to command, rule”).

Pelago is from Latin pelagus (“sea”), from Ancient Greek πέλᾰγος (pélăgos, “sea”); further etymology uncertain, possibly from Proto-Indo-European *pleh₂- (“flat”) or a non-Indo-European language.

By surface analysis, archi- (prefix meaning ‘foremost, primary’) +‎ -pelago (suffix meaning ‘sea’).

Noun sense 2.1 (“sea with many islands”) is from the fact that the Aegean Sea has many islands, and noun sense 2.2 (“group of many islands”) represents a shift of meaning from the sea to the islands in such a sea.

The verb is derived from the noun.