By Rabbi Aharon Seleh:
These four days between Yom Kippur and Sukkot are powerful days. The Imrei Pinchas quotes the Zohar that the Aura of Yom Kippur continues for three days afterwards, and Hashem continues to forgive the the Jewish nation, if he sees us elevating ourselves. The Chemdat Yomim adds that Hashem gave us the mitzvot of sukkah and lulav to help us merit a good judgement.
We really should continue saying חתמנו לחיים, since these days are like the ten days of repentance and he gives reasons why we don’t.
For many people, the final judgment will be on הושענה רבה.
The Shlah adds that these days have the status of Chol Hamoed. Many get up earlier then usual the day after Yom Kippur to show the importance of there days.
These days continue elevating us until הושענה רבה, where we hope the merit of all these mitzvot will finalize a favorable Judgement.