To be brought to this world, born in shackles she must be
The commandments of the olden days are harder than stone
Seized by the hands at youth, firmly clasped the girl's hands are
Shrouded by the caliginous night, what path is for her to take?
Although the scent lingers on, the flower shall fall
Spring has yet to embrace me; wherever could it be found?
Promises of he and I, the vows of days past
All will disappear, lost forever to the void, the pitch-black darkness
Witnessed my eyes hath, the ties of man and woman, as but frivolous;
Yet here I now agonize, as such hath befallen me
When you reached out to me, that beautiful hand of yours
How it tampered with my heart, affections held long and dear
What maketh one a woman; to be tainted, or of sin?
From the womb the red does seep; for whom such a color flows?
My goodness, how tragic
but, alas, guilty, yet
satisfied
Honestly this started with me trying to figure out what Ending 2's song title meant and then it just expanded to all the songs.
Not really a detailed analysis, more like observations and writing down the kanji meanings.
Ending 1: まよひ唄 (Mayoi uta)
迷ひ is an archaic reading of 迷い (mayoi), with definitions including "confusion", "indecision," "illusion," and "lost."
唄 (uta) is an alternate kanji from 歌 (uta), both meaning "song".
In JP Buddhism, "mayoi" refers to an inability to reach enlightenment due to lingering attachment.
The JP Buddhist term for the human realm is also called "mayoi no sekai" (world of the lost).
As you noticed, this song uses primarily archaic Japanese. both the title and lyrics are written in archaic Japanese.
Hinako's journey is very referential to Buddhism and the cycle of rebirth, as it takes at least 3 "cycles" (NG+ runs) before she reaches enlightenment (Ending 4).
The melody itself is taken from a Japanese folksong titled 花嫁人形 (Hanayome Ningyou) meaning "The Bride Doll". The folksong speaks of a bride doll weeping, yet she shouldn't cry lest it ruins her beautiful kimono. Fitting, huh?
Ending 2: つきよのいねりめ (TSUKIYONOINERIME)
Anagram of the phrase きつねのよめいり (kitsune no yomeiri), meaning "fox's wedding".
Sun showers are often associated with "fox weddings" in JP, as referenced by Kotoyuki in the ending cutscene. One explanation is it's contradictory to see rain during a clear sunny day, so it seems like a "trick" played by the foxes.
This song has the loudest "choir" of all the endings. Perhaps this represents how Tradition demands Hinako make this choice (marry and become a good wife). The voices are so loud and repetitive that it may drown out Hinako's own voice, forcing her to supress herself.
Ending 3: 七尾の黄昏 (Shichibi no Tasogare)
Shichibi is the name of the Fox Boss fought in this route, literally meaning "seven tails." Not to be confused with the Kyubi (nine-tails) in Ending 4.
黄昏 (tasogare) means "twilight", but can also refer metaphorically to "the decline of someone's life," possibly referencing to how the fox fails to stop the water dragon/geyser eruption due to losing influence/power to the Tsukumogami.
This is my speculation, but the title might also refer to how Kotoyuki loses his life's purpose by failing to marry Hinako. Unlike Ending 4, where he is freed from his family's "curse" and able to live for himself, here he is still "trapped" as the Tsuneki heir, the Shichibi.
Ending 4: 放下着 (Hougejaku)
A Zen phrase that means "let go!" including letting go of preconceptions, assumptions, and attachments.
放下 (houge) means "discarding" or "casting off".
着 (chaku), in this context, it is used similarly to an exclamation point, emphasizing the previous kanji, placing further precident on "letting go!!"
*Here's two articles discussing "hougejaku" in a modern context, I highly recommend reading it!
"Hougejaku" perfectly describes Hinako's struggles and journey. Honestly the topics of "hougejaku" and "Buddhism" in SHf's story could be made into it own discussion.
This is also the only ending song without any voices, reinforcing the themes of Hinako finally obtaining "silence" and "inner peace".
Credits song: 嘆鳥祀歌 (Bird's Lament)
嘆く (nageku) means "to lament" or "to grieve".
鳥 (tori) means "bird".
祀る (matsuru) means "to enshrine" or "to worship".
歌 (uta) means "song." This is the more commonly-used kanji in contrast to the "uta" in "Mayoi uta"
Notable in having lyrics only at the beginning before turning into primarily an instrumental track (with the sickest guitar solo imaginable):
Stained in red sunset hues lies
the hill steeped deep in silence
Now away from the birdcage,
shrouded in the fog
As this track plays only after the mid-credit cutscene, maybe it represents how whichever path Hinako chooses, the future ahead is uncertain. There is no 100% "good" or "bad" ending, and her future is one filled with both hope and anxiety. It reflects how Hinako values the choice itself before results.