Many people know the aggadeta in gemara Berakhos 26b regarding the origin of daily tefilos:
The Gemara comments: It was taught in a baraita in accordance with the opinion of Rabbi Yosei, son of Rabbi Ḥanina, and it was taught in a baraita in accordance with the opinion of Rabbi Yehoshua ben Levi. The Gemara elaborates: It was taught in a baraita in accordance with the opinion of Rabbi Yosei, son of Rabbi Ḥanina: Abraham instituted the morning prayer (shacharis), as it is stated when Abraham came to look out over Sodom the day after he had prayed on its behalf: “And Abraham rose early in the morning to the place where he had stood before the Lord” (Genesis 19:27), and from the context as well as the language utilized in the verse, the verb standing means nothing other than prayer, as this language is used to describe Pinehas’ prayer after the plague, as it is stated: “And Pinehas stood up and prayed and the plague ended” (Psalms 106:30). Clearly, Abraham was accustomed to stand in prayer in the morning.
Isaac instituted the afternoon prayer (mincha), as it is stated: “And Isaac went out to converse [lasuaḥ] in the field toward evening” (Genesis 24:63), and conversation means nothing other than prayer, as it is stated: “A prayer of the afflicted when he is faint and pours out his complaint [siḥo] before the Lord” (Psalms 102:1). Obviously, Isaac was the first to pray as evening approached, at the time of the afternoon prayer.
Jacob instituted the evening prayer (maariv/arvit), as it is stated: “And he encountered [vayifga] the place and he slept there for the sun had set” (Genesis 28:11). The word encounter means nothing other than prayer, as it is stated when God spoke to Jeremiah: “And you, do not pray on behalf of this nation and do not raise on their behalf song and prayer, and do not encounter [tifga] Me for I do not hear you” (Jeremiah 7:16). Jacob prayed during the evening, after the sun had set.
While the question is essentially similar to the question "Who instituted the Musaf prayer?", I am asking for a source in חז"ל, not commentary. Is there a similar statement in chazal (including kabbala) regarding the origin of tefilas mussaf, attributing it to either forefathers, foremothers, or the shevatim?
