It seems impossible to determine who these servants, singers, the Nethinim (“temple servants”) were. Other passages in Ezra speak of singers of the House of Asaph [a Levite descended from Kohath] (Ezra 2:41), porters of the house of Shallum (v.42), singers, porters, Nethinim (v.70).
The ones in vv.55-58 are specifically talking about Solomon’s servants, singers, etc.
In I Samuel 8 God reveals through His prophet Samuel:
“11And he said, This will be the manner of the king that shall reign over you: He will take your sons, and appoint them for himself, for his chariots, and to be his horsemen; and some shall run before his chariots. 12And he will appoint him captains over thousands, and captains over fifties; and will set them to ear his ground, and to reap his harvest, and to make his instruments of war, and instruments of his chariots. 13And he will take your daughters to be confectionaries, and to be cooks, and to be bakers. 14And he will take your fields, and your vineyards, and your oliveyards, even the best of them, and give them to his servants. 15And he will take the tenth of your seed, and of your vineyards, and give to his officers, and to his servants. 16And he will take your menservants, and your maidservants, and your goodliest young men, and your asses, and put them to his work. 17He will take the tenth of your sheep: and ye shall be his servants. 18And ye shall cry out in that day because of your king which ye shall have chosen you; and the LORD will not hear you in that day.”
Thus, many of these servants were indeed Israelites, however, the issue is that they had somehow not had their genealogies recorded or they were lost and could not PROVE they were Israel. Solomon could also have purchased Israelites as slaves, who were sold for their debts or crimes, and if Solomon gave those male servants a wife who was a slave also, the children would be Solomon’s perpetually. Solomon could have also had servants / slaves of other races.
However, since the word Nethinim [naw-theen] (a form of the name / word Nathan [naw-thahn]) means, “one given”, that is, as a Temple servant”, it seems most likely that the Nethinim had to be Israelites—for it would seem to be an abomination to have anyone in the Temple who was not an Israelite. Other pure-blooded cousin-kinsmen, like Aramaeans, other branches of Hebrews, etc., could approach to the Court the Gentiles Nations, but not the part that Israel could approach.
That is the issue. If those in question could not prove by the genealogies that they were Israel, it is quite possible (but not certain) that they had unlawful marriages (whether out of race or merely not properly attested, not approved of the parents, elopees, etc.), then the marriage would not have been recorded and thus, even if pure in their genealogies, they were not bona-fide Israelites if it could not be proved (other unlawful marriages would be too close within a family, women put away and not legally divorced, etc.; if too close familially, the offspring would be cursed). However, if they could not prove by the genealogical records that they were indeed Israelites, it seems most probable that they could no longer serve as Nethinim either. Likewise, since the Tribe of Levi was given for service, it seems most likely that the Nethinim were Levites.