No Hallel in the seder?

Question

I used a reprint of an old haggada this year (I think it was this one) on the second night. Through the meal everything was as I expected, other than a few differences because the haggada is Egyptian and I'm Ashkenazi, which were easy to work around.

After bentching was where it got really strange. The haggada had the third cup and שפך חמתך as expected, then it went right to לשנה הבאה בירושלים, the fourth cup, al hagefen, and חסל סדור פסח. The inside back cover has sefirat haomer. That's it. No Hallel at all, except the parts during Maggid. (I think they called לשנה הבאה בירושלים and the brachot before and after the fourth cup the "Hallel" section).

Where does this come from? Hallel is mentioned explicitly in the mishna, I thought everyone says it. Do they say it in shul and count that somehow (even though the mishna is pretty explicit not that way)? But then when do they say Nishmat and Hallel Hagadol?

Picture of the pages, as requested. I didn't do a good job taking the last picture, but you can still make it out (at least the Hebrew parts, maybe not the French. The sefirat haomer page was also smudged to begin with.). The only thing after this is a couple of pages about the Diskin orphan home, which obviously weren't in the original.

Answer 1

According to the Oz V’hadar extended Mesivta Haggadah, it’s a machlokes Rishonim as to whether we say Hallel HaGadol or not:

• According to the reading of Rashi and Rashbam, R’ Tarfon adds to the Mishnah when he says we say Hallel HaGadol. Many Rishonim, including Tosfos and Ra’avya accordingly hold that since it’s a Machlokes Amoraim as to what Hallel HaGadol is, that indicates that we pasken like R’ Tarfon.
• Many Geonim and Rishonim, including Rav Sa’adya, Rabbeinu Chananel, and the Ba’al HaMeor, understand that R’ Tarfon, who in their reading proposes Hallel HaGadol on a fifth cup, is arguing on the Mishnah. Since they’re arguing, the Halacha follows the majority opinion of the Mishnah which says not to say Hallel HaGadol.
• Still other Rishonim, including the Raavad, the Ramban, and the Ran, take a middle ground: the fifth cup is optional, and Hallel HaGadol is only said if one drinks the fifth cup.

You and I apparently hold like the first opinion, that we say Hallel HaGadol without a fifth cup. Perhaps the printers of that Haggadah held like the second opinion, not to say Hallel HaGadol, and also held that the regular Hallel is to be said in shul.