On a simple level, it is stated by Rabbi Yaacov Tzvi Yolles in Sefer Kehillat Yaacov, ערך שב: שבת:ב that the change in the text for Shabbat is because we follow what the angels did on the first Shabbat.
בשבת בראשית קרא הקב״ה אל המלאכים ומינה אותם על העולם פתחו כולם ואמרו הכל יודוך לכך אומרים בשבת הכל יודוך
The opening words of the weekday version emphasizes G-d's flow of blessing and maintenance into the creation, like with the phrase:
המאיר לארץ ולדרים עליה, ברחמים כו׳
The One who radiates to the earth and to those who dwell upon it, in mercy...
The emphasis is the flow from Above to Below. In the language of kabbalah, this is referred to as אור ישר, direct light.
In the text for Shabbat, the primary focus changes directions, like with the phrase:
הכל יודוך, והכל ישבחוך, והכל יאמרו כו׳
Everything acknowledges You, and everything praises You, and everything says...
The emphasis is from Below to Above. In the language of kabbalah, this is referred to as אור חוזר, returning light.
Another word for return is תשובה which shares the same root as Shabbat (שבת). It is worth pointing out that this idea of sharing the same root is not in the sense of common grammar, but as explained, for example, in ספר קל״ח פתחי חכמה by Rabbi Moshe Chaim Luzzato in the section ענין האותיות והשמות: פתח יח-כא. That each letter is the manner in which this flow of blessing expresses from Above, how it is rooted Above.
And this is one of the ideas emphasized in the words of the kiddush said on Shabbat night.
ויקדש אתו, כי בו שבת מכל-מלאכתו כו׳
And He sanctified it, because all His work returned to Him...
And this follows the concept mentioned by the Alter Rebbe in מאמרי אדמו״ר הזקן: אתהלך לאזניא which is quoting Pri Etz Chaim:
ונזכר בפרי עץ חיים שבירורי דכר בו׳ ימי החול ובשבת שהוא בחינת מלכות אין
בירורים כי אם עליות כו׳.
This idea is discussed more fully by the Alter Rebbe in his Chassidic discourse which opens with the words: קודש ישראל לה׳ ראשית תבואתה וגו׳ which is found in the same sefer.