Menuchah as the true defeat of Amalek

מה שקבעו עיקר היו"ט ביום המנוח ואומרים שעשה נסים בזמן הזה.

As to why they fixed the essence of the Yom Tov on the day of rest (menuchah), and we say "[He] performed miracles at this time."

The Sefas Emes asks why Purim is established specifically on the day of rest after the fighting, the fourteenth and fifteenth, rather than on the day of battle itself.

הגם דלכאורה עיקר הי' נצחון המלחמה.

Even though, seemingly, the main event was the victory in the war.

One would have thought the day of actual triumph in battle should be the central celebration.

אכן תכלית מלחמת עמלק ימ"ש הוא לבטל המנוחה.

However, the very aim of Amalek's war — may his name be blotted out — is to nullify menuchah (rest, tranquility).

Amalek's whole purpose is to destroy stillness and tranquility, to keep Bnei Yisrael from ever reaching rest.

כמ"ש אשר קרך בדרך.

As it is written: "who happened upon you on the way (asher karcha baderech)."

Amalek struck "on the way," disrupting Bnei Yisrael while they were still in motion, before they could settle into menuchah.

כמ"ש והיה בהניח כו' תמחה כו'.

As it is written: "And it shall be, when [Hashem] gives you rest (b'haniach)... you shall blot out," etc.

The very mitzvah to erase Amalek is tied to the time when Hashem grants menuchah — for rest is precisely what Amalek opposes.

נמצא שעיקר רדיפת עמלק שלא לבוא אל המנוחה.

It emerges that the essence of Amalek's pursuit is to prevent [Bnei Yisrael] from arriving at menuchah.

Amalek's relentless pursuit is aimed entirely at blocking the arrival of rest and tranquility.

וזה האות שבאו אל המנוחה הוא עדות על מחיית כחו של עמלק.

And this — that they reached menuchah — is the sign and testimony to the blotting out of Amalek's power.

Attaining rest is itself the proof that Amalek's strength has been erased, since rest is the very thing he fought to prevent.

ובזאת המנוחה מחו אותו יותר מבמלחמה.

And through this menuchah they blotted him out more than through the war.

The achievement of rest erases Amalek even more completely than the physical battle did.

ולכן כתיב ונוח מאויביהם והרוג כו' שבמנוחה זו הרגו אותו.

Therefore it is written, "and they had rest (v'noach) from their enemies, and they killed," etc. — for through this very rest they slew him.

The verse joins "rest" and "killing" because it was specifically in attaining menuchah that Bnei Yisrael truly destroyed Amalek.

והענין דכתיב מחה אמחה דרשו חז"ל בעוה"ז ובעוה"ב למטה ולמעלה כו'.

And the matter is that it is written "I will surely blot out (macho emcheh)," which Chazal expounded as: in this world and in the World to Come, below and above, etc.

The doubled language teaches that Amalek must be erased on two planes — the physical world below and the spiritual root above.

ולעולם כן הוא שבמלחמה התישו כחו בגשמיות כדי שיבואו אל המנוחה.

And it is always so: in the war they weakened his strength in the physical (b'gashmius) in order to come to menuchah.

The battle works on the lower, physical plane — sapping Amalek's material power as a means toward reaching rest.

ואז שבאו לשורשם הרגו את השורש שלו למעלה וזה העיקר ועשו אותו יום משתה ושמחה כנ"ל:

And then, when they came to their own root, they killed his root above — and this is the essential point — and they made that day one of feasting and rejoicing, as above.

Once Bnei Yisrael return to their spiritual root through menuchah, they destroy Amalek's root above — the deeper victory — and therefore the day of rest, not the day of battle, was set as the feast of Purim.

Summary: Purim is celebrated on the day of rest because Amalek's entire aim is to deny Bnei Yisrael menuchah. Reaching rest is the true sign that his power has been erased. The physical battle only weakened Amalek below; it was in attaining menuchah and returning to their root that Bnei Yisrael struck his root above — the essential victory — which is why the day of rest, with feasting and joy, was made the heart of the Yom Tov.