The Luchos bind physical to spiritual

ובפסוק והלוחות מעשה אלקים המה כו' חרות כו'.

And on the verse, "And the Tablets were the work of Hashem... engraved..." (Shemos 32:16).

The Sefas Emes takes up the description of the Luchos (Tablets) as the very "work of Hashem," with the word charus (engraved) written upon them.

ודרשו חז"ל חירות כו'.

And Chazal expounded: do not read "charus" (engraved) but "cheirus" (freedom) (Avos 6:2).

Our Sages reread the word charus as cheirus — freedom — teaching that the Luchos brought true liberation.

הענין הוא דאיתא כתב המכתב נברא בע"ש ביה"ש.

The matter is as it is taught: the writing and the script were created on Erev Shabbos at twilight.

The Mishnah (Avos 5:6) lists the writing of the Luchos among the ten things created at the very end of the six days of Creation, at twilight before the first Shabbos.

כי יש להעשי' מדריגות.

For there are levels within "doing" / the act of Creation.

The world of asiyah (action, the realm of "making") has gradations — some made things are loftier and closer to their source than others.

לכן נברא אדם באחרונה כדי שיכנוס לשבת מיד כו' ע"ש.

Therefore Adam was created last, so that he would enter into Shabbos immediately, see there.

Man, the pinnacle of Creation, was fashioned last specifically so he could step straight into Shabbos — showing his special bond to the highest rung.

פי' שהוא מובחר מכל מעשה בראשית.

The meaning is that he is the choicest of all of Creation.

Adam is the select, most refined of all created things in Maaseh Bereishis (the work of Creation).

ויש לו התקשרות לשורש הבריאה.

And he has a connection to the root of Creation.

Because he is the choicest, man is bound to the inner root from which all of Creation flows.

והוא השבת שיש בו עלי' לכל הברואים.

And that is Shabbos, in which there is an elevation for all created things.

That root is Shabbos, the day on which every creature is uplifted back toward its source.

והשורש נקרא מעשה אלקים שאינו גשמיי ככל העשי'.

And the root is called "the work of Hashem," which is not physical like the rest of "doing."

This inner root is the "maaseh Elokim" — a non-physical dimension, unlike the rest of the material world of asiyah.

והוא כח ממוצע בין מעשה גשמיי לרוחניי שהוא כח אלהות כמ"ש מפליא לעשות שמקשר גשמיי ברוחניי ע"ש [ברמ"א או"ח בברכת אשר יצר].

And it is an intermediate force between the physical act and the spiritual, which is a Divine power, as it is written "Who acts wondrously" — that He binds the physical to the spiritual, see there [in the Rema, Orach Chaim, in the blessing of Asher Yatzar].

This root is a "go-between" power linking the material and the spiritual — a power of G-dliness. The Rema explains the phrase "mafli laasos" (Who acts wondrously) in the Asher Yatzar blessing as the wonder of how the soul (spiritual) is bound within the body (physical).

הכלל כי זה הכח נקרא שורש העשי'.

The principle is that this force is called the root of "doing."

In short: this intermediate, G-dly power is the very root and source of the entire realm of action.

וע"ז רמזו שנברא בע"ש שיש בו תערובות ב' הכחות מהשבת ומהמעשה.

And to this they alluded by saying it was created on Erev Shabbos, which contains a blending of the two powers — of Shabbos and of the weekday act.

Twilight of Erev Shabbos is itself the meeting point of Shabbos and the week — fittingly, the writing of the Luchos was created precisely then, since it embodies the fusion of the spiritual (Shabbos) and the physical (asiyah).

וזכו בנ"י בלוחות ראשונות לתקן כל העשיה שיהיה להם דביקות בשורש.

And Bnei Yisrael merited, through the first Luchos, to rectify all of "doing," so that they would have a deveikus (cleaving) to the root.

With the first Luchos, Bnei Yisrael attained the power to elevate all worldly action and bind it back to its inner root in deveikus.

וממילא הי' חירות בכל:

And consequently there was freedom in everything.

Once all of action was reconnected to its root, true cheirus (freedom) was present in everything — this is the deeper meaning of the Luchos as "cheirus."

Summary: The Luchos are called "the work of Hashem" because their writing belongs to the intermediate, G-dly power that binds the physical to the spiritual — the very root of all action, alluded to by its creation at the Erev Shabbos twilight where Shabbos and weekday meet. Through the first Luchos, Bnei Yisrael could elevate all of asiyah back to its root, and so charus became cheirus — true freedom in everything.