Since when is Hoshana Rabba special and different from the rest of Chol HaMoed? In the Torah it doesn’t seem to be mentioned as anything special.
Although the Torah doesn’t differentiate between the 7th day of Sukkot and the previous 5 days of Chol HaMoed, we know that all of the time elements revolve around the number 7 (Shabbat, Shmitta, Yovel, etc.). Just as Pesach (the seventh month from Tishrei) has 7 days and then 7 weeks (Omer) and then the 8th week begins with Shavuot which is accordingly called Atzeret (the “end” of Pesach), similarly, there are 7 days of Sukkot (in the 7th month from Nissan) before the special 8th day which is also called (Shmini) Atzeret. Accordingly, it’s logical that the 7th day, Hoshana Rabba, also be special. The taking of the Arava and special tfilot before beating the Hoshanot on Hoshana Rabba was an early decree of the later prophets (Hagai, Zecharia and Malachi) more than 2,500 years ago which probably reflected a previously known uniqueness for that day. Being that “everything follows the ending” (Brachotb12a), it’s logical that almost 2 months of tshuva and special prayers for our judgement and appeals spanning Elul, Rosh HaShana, 10 Days of Tshuva and Yom Kippur, be capped off with one last chance to appeal. Also, we are judged on Sukkot for the coming year’s rainfall (Mishna Rosh HaShana 1, 2), but we don’t want to ask for rain which would chase us out of our Sukka, so we relate to this judgement on Hoshana Rabba, the last possible time in Sukkot.