Where can I find sources about the history of the piyutim מי אדיר and מי בן שיח, which usually get sung at Ashkenazi weddings under the chuppah when the groom and bride walk in?
Some sources mentioned in Aryeh Kaplan, Made In Heaven, pp. 156;161– Dr. ShmuelAug 16, 2020 at 20:39
This article explains,
The Zohar (Bereishit 226) says that when a person wants to bless his son or friend, etc., he should first bless Hashem — otherwise, the blessing will not be long-lasting.
Since the Chatan and Kallah will be blessed under the Chuppah with seven berachot, a hymn is first sung that consists of praises of Hashem. In it we also pray that He confirm the blessings that will soon be recited for the Chatan and Kallah.
(שלחן העזר סי' ז' סעי' ד' סק"ו, ועי' נדרים ל"ב ע"ב)
The author of the hymn is unknown, but some say that it was written in the late 15th century by the same person who composed the hymn “Adir Hu” which many recite at the Pesach Seder. The earliest printed source of this hymn is in the Birkat Hamazon, Dyherenfurth, 1791.
(אוצר כל מנהגי ישרון סי' ט"ז)
Interestingly, Rav Moshe Heinemann (Shidduchim-Sheva Berachos 6:30) writes
מי אדיר talks about the one who is more blessed, is greater, and stands out among everyone and everything - going through the aleph-beis with praises. We’re not talking about the Ribono Shel Olam. We’re talking about the Mesader Kiddushin who is being מברך the chosson v’kallah. Then when the kallah walks down to the chuppah, we say מי בן שיח based on a Chazal that if there are ten people together but only one of them knows the Sheva Berachos, we call that one person כְּשׁוֹשַׁנָּה בֵּין הַחוֹחִים (Shir HaShirim Rabba 2:2) – he’s like a rose between the thorns of people who don’t know anything. Who is the מי בן שיח - who can say the berachos? The Mesader Kiddushin. We sing these for the kovod of the Mesader Kiddushin so the chosson and kallah feel they are so חשוב to have such a special Mesader Kiddushin.
You just beat me to it! The mi bon siach source that you bring is first brought down in the Machzor Vitri basing it off the medrash in Shir HaShirim Rabbah that you mention. The way the sefer yismach leiv by Rav Menachem Savitz explains it, is that everyone in the wedding feast are unable to say bircas chassanim, and then one enters who can. He is like the rose among thorns as he is "מי בן" - i.e. he is מי שמבין, someone who understands, "שיח" how to make the brachos and therefore is "שושן חוחים" a rose among thorns– DovAug 16, 2020 at 22:34