Understanding Hallel from Pesachim 118

מאי טעמא אמרינן האי משום שיש בו חמשה דברים הללו יציאת מצרים קריעת ים סוף ומתן תורה ותחיית המתים וחבלו של משיח

what is the reason that one also recites this hallel of Psalms 113–118, the section recited on every joyous occasion? The Gemara answers: The reason is because the regular hallel contains these five matters: The remembrance of the exodus from Egypt, the splitting of the Red Sea, the giving of the Torah, the resurrection of the dead, and the pangs of the Messiah. Since it mentions these key concepts, this hallel is also considered important.

יציאת מצרים דכתיב בצאת ישראל ממצרים וקריעת ים סוף דכתיב הים ראה וינוס מתן תורה דכתיב ההרים רקדו כאילים תחיית המתים דכתיב אתהלך לפני ה׳
The Gemara elaborates: The exodus from Egypt, as it is written: “When Israel came forth out of Egypt, the house of Jacob from a people of strange language” (Psalms 114:1). And the splitting of the Red Sea, as it is written: “The sea saw it and fled; the Jordan turned backward” (Psalms 114:3). The giving of the Torah, as it is written: “The mountains skipped like rams” (Psalms 114:4), which is similar to the description of the giving of the Torah found elsewhere in the books of the Prophets. The resurrection of the dead, as it is written: “I will walk before the Lord in the lands of the living” (Psalms 116:9), which follows the verse: “For you have delivered my soul from death.” After mentioning death, the psalm describes the resurrection in the lands of the living.
חבלו של משיח דכתיב לא לנו ה׳ לא לנו ואמר רבי יוחנן לא לנו ה׳ לא לנו זו שעבוד מלכיות איכא דאמרי אמר רבי יוחנן לא לנו ה׳ לא לנו זו מלחמת גוג ומגוג
The pangs of the Messiah, as it is written: “Not to us, God, not to us, but to Your name give glory” (Psalms 115:1). And Rabbi Yoḥanan said: The verse “Not to us, God, not to us” and the entire psalm, including the verse “Why should the nations say, where now is their God?” (Psalms 115:2), is referring to the era of the enslavement of the kingdoms and the redemption of the Jewish people from their dominion. Some say that Rabbi Yoḥanan said: The verse “Not to us, God, not to us” is referring to the war of Gog and Magog, the catastrophes and wars that will befall the Jewish people in the end of days from which they will be delivered.
רב נחמן בר יצחק אמר מפני שיש בו מילוט נפשות של צדיקים מגיהנם שנאמר אנה ה׳ מלטה נפשי חזקיה אמר מפני שיש בו ירידתן של צדיקים לכבשן האש ועלייתן ממנו
Rav Naḥman bar Yitzḥak said: Another reason why one recites hallel of Psalms 113–118 is because it contains a reference to the deliverance of the souls of the righteous from Gehenna, as it is stated: “I beseech you, Lord, deliver my soul” (Psalms 116:4). Ḥizkiya said: Another reason is because it contains the story of the descent of the righteous Hananiah, Mishael, and Azariah into the fiery furnace and their miraculous ascent from it.