So I’m not sure how familiar you might be with the projection of power in pre-contemporary Europe, but I’ll start with a few basic notions. While defense (that is to say self-preservation) is a well-accepted role of governing institutions, is it not a necessary condition. It can take different shapes, be managed ad-hoc, or be absent altogether. In Post-Roman Europe, very generally the manpower and skills needed for defense were linked to privilege, and most commonly this privilege was the ownership of land. Thus the duty of soldiering went from being a salaried, “standing” profession (as had occurred during the roman empire, and not reappear in Europe until the early modern period) to being a “domestic chore” - whereby a component of land ownership, and privileges associated with land ownership, was the expectation that male members of the household own and know how to use arms and armor.
We can avoid the weeds of this exact relationship - there were gray areas where large landowning (“aristocratic”) households could and did retain salaried or otherwise “professional” soldiers in their household, and there were also variations in the precise nature of how governments - be they the emergent monarchies or more local systems of government, recruited fighting men (and we can get more into this in a follow-up if you’re interested).
First and foremost, we would need to understand when precisely we are examining the vicissitudes of the Republic of Genia. Because over the course of the 16th-17th centuries, Genoa did develop a standing professional army with characteristics largely analogous to those appearing in much of the rest of Europe in the same period.
But I can guess with near-certainty that you are more interested in an earlier period, when the Republic of Genoa was at its height and very far away from developing the sort of “formalized” efficiencies which began emerging in early modern society. And we do see dynamics in Genoa analogous to the kind of warrior-landowner (or “Warrior-Aristocracy”) analogous to those in the rest of Europe: the Italian cities conveniently (but not completely) substituted the monarchs of the rest of Europe as centers of authority and political organization, but this didn’t mean that a privileged landowning class didn’t emerge. Thus even along the Ligurian coast (much like other parts of Italy, coastal or otherwise) aristocratic landowners leveraged rents and privileges from their renters (although, to be fair, in Italy they had to contend with a uniquely powerful rival landowning institution: the church). These landowners not only formed an important component of the “urban” aristocracy which populated urban institutions (in some parts of Italy, rivalries between city-based and rural-biased aristocrats did emerge, but in Genoa like in many other successful cities, the two aristocratic vocations coexisted fairly harmoniously) and this sort of landowning class was also tasked with the Genoese community’s power projection.
Unlike other Italian cities, like Milan and Bologna, where important aristocratic dynasties were invested with longstanding formal responsibilities to arm the citizenry, Genoa’s geographic isolation (shielded, at its shoulders, by mountains) and relative size relative to its neighboring communities along the coast did not create an analogous need. But landowners, some with feudal or semi-feudal investiture, were nonetheless the backbone of Genoese power projection. Not only were they the primary financiers and organizers of the mercantile expeditions on which the city’s wealth was built, but ownership of arms and armor, and armed retinues made of relatives, friends, and other hangers-on, could be found in genoese aristocratic households and would form the first line or aggression and defense for the city. Costal communities in Liguria, while not without exceptions, could expect to feature a fortress or grand house inhabited by one of these aforementioned genoese aristocratic dynasty, with some sort of privilege or investiture tied to the surrounding area, and also generally projecting force and authority. In this regard, Liguria was actually fairly “Feudal” and rural life does resemble France or Germany (apart from the differences in climate, diet, and economic activity - and we can also get into this in a follow-up as well).
In the grand military expeditions organized by the Republic, this group of people would continue to form the backbone of power projection. The people could be expected to construct and arm galleys and themselves lead expeditions down the coast, or across the sea to Corsica, Sardinia, or Greece, to combat threatening or uncooperative communities and secure their submission and with it, safe passage and harbor for Genoese trade. But they would also be involved in broader efforts as well: it is from this class of people that the “Capitani del Popolo” (typically two) would be extracted to lead military efforts, and this group of people would also populate the broader military hierarchy.
But even in these broader efforts, like in conflicts against Pisa, Venice, and the Crown of Aragon, the genoese naval fleet reflected the typical composition of military power all over medieval Europe: There was no “standing” fleet, with few purpose-built war vessels featuring in a fleet largely composed of commandeered merchant vessels.
The genoese war fleet was likewise manned in an ad-hoc form. Sometimes when ships were commandeered the crew would follow, especially if the ship was already owned by a genoese aristocratic dynasty. Most crew members would be sailors, but mercantile vessels also could be expected to have one or more crew members trained in the use of arms (and this became increasingly common as naval competition grew, which ships coming to have increasing numbers of crew members exclusively dedicated to security). But while there could be expected to be a small roster of war-ready individuals to call on, in times of war the largest cohort the genoese relied on would be citizen-volunteer crews. Additionally, in times of most need coastal communities subjugated by Genoa would also be tasked to provide a certain number of ships and crew, and in these cases the communities were left to decide on their own how to provide what was asked of them. Those conscripted in this manner, both in Genoa and surrounding communities, were typically upper middle class and would also generally be able to provide their own arms and armor. While they might be salaried for the duration of the campaign, they could also be contracted by promoting a portion of the plunder (unsurprising, given the Genoese naval military tradition had in significant part been built on a history of piracy).
So to finally reach the crux of your question, when I mentioned above that the genoese could commandeer ships whole sale with all or part of their crews, these instances could definitely see foreigners conscripted which we might nowadays class as “Mercenaries;” these would be individuals which had been hired with the express task of protecting the cargo with no regard to their nationality, and when commandeered they would follow the ship to war. But generally, the Genoese armed forces relied on citizen-soldiers (usually freely contracted) and an organizational backbone made up of the city’s own aristocracy.