Humility draws the Shechinah's joy

אחר יוה"כ חג הסוכות דכ' ויספו עטים בה' שמחה רומז לחג האסיף שזכו בנ"י לבחי' ענוה ביוה"כ במצות ועניתם.

After Yom Kippur comes Chag HaSukkos, of which it is written, "and the humble (anavim) shall add joy in Hashem" — alluding to the Festival of Ingathering, for Bnei Yisrael merited the aspect of humility on Yom Kippur through the mitzvah of "you shall afflict [your souls]."

The Sefas Emes reads the pasuk in Yeshayahu about the anavim rejoicing as a hint to Sukkos, the harvest festival; the self-affliction (innui) of Yom Kippur instills anavah, and from that humility the joy of Sukkos flows.

והוא בחי' מרע"ה ענוה גדולה מכולם.

And this is the aspect of Moshe Rabbeinu, whose humility was greater than all.

The trait of anavah belongs supremely to Moshe Rabbeinu, the most humble of all men.

בר"ה בחי' יראה ויוכ"פ בחי' ענוה דכ' עקב ענוה יראת ה'.

Rosh Hashanah is the aspect of fear, and Yom Kippur is the aspect of humility, as it is written, "the consequence of humility is the fear of Hashem."

The Days of Awe ascend in order: Rosh Hashanah instills yirah, and that fear leads onward to the anavah of Yom Kippur, as Mishlei pairs humility with yiras Hashem.

יראה מביא לידי ענוה ואמרו חז"ל בגסות אמר הקב"ה אין אני והוא יכולין לדור.

Fear brings one to humility; and Chazal said concerning the arrogant, the Holy One declared, "I and he cannot dwell together."

Yirah produces humility, while the opposite — gasus haruach, arrogance — drives away the Shechinah, for Hashem says He cannot share a dwelling with the haughty.

א"כ בסוכות שזוכין בנ"י למצות סוכה דחל שם שמים על הסוכה ואומרים אני והו.

If so, on Sukkos, when Bnei Yisrael merit the mitzvah of sukkah, the Name of Heaven rests upon the sukkah, and we say "Ani vaHo."

Having acquired humility, Yisrael can now host the Shechinah: the divine Name dwells upon the sukkah, and in the Hoshanos we invoke "Ani vaHo," names of Hashem associated with His indwelling presence.

וכמו שאין הקב"ה דר עם גסי הרוח כמו כן ענוים צריכין דירה מיוחדת.

And just as the Holy One does not dwell with the arrogant, so too the humble require a special dwelling.

The flip side of Hashem's refusal to dwell with the proud is that the humble, who can host Him, need a dwelling set apart for that purpose — the sukkah.

ומרע"ה עניו מכל אדם כו' על פני האדמה ולכן נתעלה לשמים שלא הי' יכול לדור למטה.

And Moshe Rabbeinu was "the most humble of every man... on the face of the earth," and therefore he was elevated to heaven, for he could not dwell below.

Moshe's unmatched humility lifted him beyond this world; his very anavah made earthly dwelling too confining, and he ascended to receive the Torah in the heavens.

מעין זה בנ"י ענוי ארץ יותר מכל האומות וצריכין סוכה ודירה מיוחדת להיות מובדלים מגסי הרוח.

In a similar way, Bnei Yisrael are the humble of the earth more than all the nations, and they need a sukkah and a special dwelling, to be set apart from the arrogant.

Yisrael shares a measure of Moshe's anavah, exceeding the nations in humility; therefore they too require the set-apart dwelling of the sukkah, separating them from the proud.

ולפי שענוים זוכין להשראת השכינה כמ"ש אשכון את דכא לכן הם שמחים דהשמחה במעונו:

And because the humble merit the resting of the Shechinah, as it says, "I dwell with the contrite," therefore they are joyful, for "joy is in His dwelling."

Humility draws the Shechinah, as Hashem says He dwells with the lowly of spirit; and since "the joy is in His dwelling place," the humble who host His presence are filled with the simchah of Sukkos.

Summary: The innui of Yom Kippur cultivates anavah — the supreme trait of Moshe Rabbeinu — and from that humility flows the joy of Sukkos. Rosh Hashanah's yirah leads to Yom Kippur's humility; while arrogance drives the Shechinah away, the humble draw it near. So Yisrael, the humblest of the nations, needs the set-apart dwelling of the sukkah, where the Shechinah rests and "the joy is in His dwelling."