From recently reading "Why We Pray What We Pray" by Rabbi Dr. Barry Freundel, I learned that the "Nishmat" prayer, usually associated with Shabbat and Festival morning services, was originally part of the Passover Seder and only got added to the morning services during the medieval period.
Specifically it references the Mishnah Pesachim 10:7. The book translates this slightly differently from the linked website saying: "They filled the third cup for him. He then recites grace after meals. Over the fourth cup he concludes the Hallel and recites the blessing of the song." The Talmud Bavli then clarifies this with: "What is the Blessing of the Song? Rav Judah said: 'They shall praise Thee, O Lord our God'; Rabbi Johanan said: 'The soul of all that lives' [i.e. Nishmat]."
My questions are:
1) What prayer is Rav Judah referencing? It sounds like Hallel, but aren't we discussing what is immediately after that?
2) Is Nishmat still commonly part of the haggadah? None of my printed haggadot list this prayer, even the ones that include a Birkat HaMazon and a complete Hallel. It can be found here a little past 3/4 of the way down the page. Is it commonly left out, or do I just have a collection of incomplete haggadot (some of them 50 years old)?
Edit: I did eventually find it in a 1966 haggadah of mine from Rabbi Nathan Goldberg.