Death continued to stare at the emperor with his cold, hollow eyes, and the room was fearfully still. Suddenly there came through the open window the sound of sweet music. Outside, on the bough of a tree, sat the living nightingale. She had heard of the emperor’s illness, and was therefore come to sing to him of hope and trust. And as she sung, the shadows grew paler and paler; the blood in the emperor’s veins flowed more rapidly, and gave life to his weak limbs; and even Death himself listened, and said, “Go on, little nightingale, go on.” --From "The Nightingale" by Hans Christian Anderson, 1848.
"Was come" is an old fashioned structure similar in function to past perfect, but which has disappeared from English. It was mostly used to refer to something before the current point in a simple past narrative, but so near to it in time that it was effectively still part of the narrative.
Today, we would say, "She had heard of the emperor's illness, and had therefore come to sing to him of hope and trust."
In the simple past thread of the narrative here, music came in through the window. The bird hears of the emperor's illness and comes to the window before that point, so neither "hear" nor "come" can be in the simple past. We can infer that "come" happened within the time of the narration itself, so the author chose "was come". Today "had come" would be the only choice.
Also note that Andersen was Danish and wrote the tale in his native language. This may be relevant, because, as the accepted answer (by @rjpond) to the linked question states:
Interestingly, if you study French, German or Danish you'll find that a small number of verbs (generally including the equivalents to "come", "become", "rise", "fall") form their perfects with the equivalent to "be", while all the rest form perfects with the equivalent to "have".
A look at the original confirms that this is true here:
Da lød i det samme, tæt ved Vinduet, den deiligste Sang: det var den lille, levende Nattergal, der sad paa Grenen udenfor; den havde hørt om sin Keisers Nød, og var derfor kommet at synge ham Trøst og Haab; og alt som den sang, bleve Skikkelserne mere og mere blege, Blodet kom raskere og raskere i Gang i Keiserens svage Lemmer, og Døden selv lyttede og sagde: »bliv ved lille Nattergal! bliv ved!«
So it is possible that the literal translation of "var kommet" as "was come" was chosen over "had come" to stay close to the original. But of course, as others have noted, this choice would probably not be made today, because "was come" does sound oddly archaic.
It depends on how you look at it. It's a bit tricky since "was...come" isn't really in usage anymore. It's an old-timey way of saying it that you generally only run into in old writing, like scripture, Christmas carols, etc.
Anyway, technically, it's being used as a linking verb to link the subject "she" to a predicate adjective, "come" being a past participle employed adjectivally in a phrase that serves as a predicate adjective. That said, what "was come" in that sentence actually means is "came," so you could say that it's being used as an idiom to mean "came" (i.e., not just "come" but the phrase "was...come" being what's used to mean "came").