Joyful avodah seals the kapparah

אחר יוהכ"פ ימי שמחה דכ' אכול בשמחה לחמך כו' יינך כי כבר רצה האלקים כו'.

After Yom Kippur are days of simchah, as it is written, "Eat your bread with joy… your wine, for Hashem has already favored your deeds." (Koheles 9:7)

The days following Yom Kippur are joyful ones; the Sefas Emes asks about the posuk in Koheles that links eating in simchah to Hashem having "already" accepted what we do.

מאי לשון כבר.

What is the meaning of the word "already" (kvar)?

The Sefas Emes is bothered: how can the posuk say Hashem has "already" favored our deeds — before we have even done the avodah of simchah it describes?

אך באמת בנ"י עיקר בקשתם מחילה וסליחה כדי שיוכלו לעבוד השי"ת בלב טהור כמ"ש עמך הסלחחה למען תורא.

But in truth, the essential request of Bnei Yisrael is mechilah and selichah (pardon and forgiveness), so that they may be able to serve Hashem with a pure heart, as it is written, "For with You is forgiveness, so that You may be feared." (Tehillim 130:4)

What Bnei Yisrael really want from teshuvah is not merely to escape punishment, but to be cleansed so they can serve Hashem with a pure lev and renewed yiras Shomayim.

ולכן אחר יוהכ"פ שנתכפרו העונות ונטהרו נפשות בנ"י יש לקחת לעבודת הש"י בשמחה.

And therefore, after Yom Kippur, when the sins have been atoned and the souls of Bnei Yisrael have been purified, one must take [oneself] to the avodah of Hashem with joy.

Once Yom Kippur has cleansed us, the natural response is to throw ourselves into avodas Hashem with simchah, using the fresh purity we have just been granted.

לחמך יינך הוא תורה ומצות.

"Your bread, your wine" — this is Torah and mitzvos.

The "bread and wine" we are to enjoy are a moshol for Torah and mitzvos, the true nourishment of a Jew, now to be served with joy.

וע"י שעובדין אח"כ בשמחה הוא סימן שבקשת הסליחה הי' לשם שמים.

And through the fact that they afterward serve [Hashem] with joy, it is a sign that the request for forgiveness was for the sake of Heaven.

The joyful avodah after Yom Kippur retroactively proves that the teshuvah was sincere — done l’shem Shomayim — and not merely out of fear of consequences.

והקב"ה שרואה עתידות מצרף עבודת האדם אחר הכפרה לכפר לו בזכות זה.

And the Holy One, who sees the future, joins a person’s avodah after the atonement to atone for him in the merit of this.

Because Hashem sees what we will do, He counts our future joyful service as part of the kapparah itself, so the sincerity yet to be shown already strengthens the forgiveness.

וזהו כי כבר רצה שזו עבודה בשמחה כבר נתקבל לפניו יתברך:

And this is "for He has already favored" — that this avodah done in joy was already accepted before Him, Blessed is He.

This resolves the word "already": the joyful avodah after Yom Kippur was, in Hashem’s timeless foresight, "already" accepted at the moment of atonement, retroactively sealing the forgiveness.

Summary: The joyful avodah of Torah and mitzvos that Bnei Yisrael take on after Yom Kippur proves that their request for forgiveness was l’shem Shomayim; and because Hashem sees the future, He folds that future joy back into the kapparah itself — which is why the posuk can say He has "already" favored our deeds.