Shabbos As Revealed Geulah

ומ"ש בשבת וזכרת כי עבד כו' ע"כ צוך כו' לעשות כו' השבת המהר"ל פי' שזה טעם על שהשבת מיוחד לבנ"י דוקא

As for what is stated in connection with Shabbos, "And you shall remember that you were a slave [in the land of Mitzrayim]... therefore Hashem your God commanded you... to keep the Shabbos" (Devarim 5:15) — the Maharal explains that this is the reason why Shabbos is set apart for Bnei Yisrael in particular.

The Torah ties the mitzvah of Shabbos to our having been slaves in Mitzrayim, and the Maharal teaches that this is precisely why Shabbos belongs uniquely to Bnei Yisrael, who were redeemed.

אך גם בקידוש אומרים זכר ליצ"מ והוא כנ"ל שבשבת יש בחי' גאולה שמתגלה התחדשות תוך הטבע כנ"ל:

Yet in the Kiddush as well we say that Shabbos is "a remembrance of the exodus from Mitzrayim," and this accords with what was said above: that on Shabbos there is an aspect of geulah, in that the renewal hidden within nature becomes revealed, as was explained above.

The same theme appears in Kiddush, where Shabbos is called a remembrance of Yetzias Mitzrayim, because Shabbos itself carries an aspect of geulah in which the hidden, ongoing renewal within creation comes to light.

Summary: The Sfas Emes notes that the Torah links the keeping of Shabbos to Bnei Yisrael's slavery in Mitzrayim, and cites the Maharal that this connection is what makes Shabbos uniquely the inheritance of Bnei Yisrael. He then points to the parallel language in Kiddush, where Shabbos is described as a remembrance of Yetzias Mitzrayim. This is no mere historical reference: Shabbos contains an aspect of geulah, for on it the renewal that Hashem hides within nature becomes revealed. Just as the exodus uncovered Hashem's hand within the natural order, so too Shabbos reveals the continual chiddush concealed in creation.