This connection is: During the six days of creation (and the six days of the week) Hashem’s Kingship expresses itself in being drawn down to create and give life to the worlds; as we find that on the first day of creation “Hashem said let there be light and there was light”, on the second day He said “let there be a sky” and there was a sky, on the third day Hashem said “the earth cover itself with plant-life” and it happened etc., all of these acts of creation happen during the six days of the week called “the days of creation”,
and on Shabbos there is the aspect of resting from work and creation, which is the idea of “אָּח ורְדַׁאָּחיְי נ-rest and relaxation”, which is the time when the worlds ascend above to receive life from their source, instead of their source needing to come to down to enliven them, just like a person who ceases from work and rests, that all his energy invested in his work goes up and back into himself when he rests from his work.
So too regarding the involvement and worry in obtaining livelihood and other material matters, which are called “many waters”, when they become transformed and reconnected to Hashem in revealed manner through the person’s prayers, this is called “אָּח ורְדַׁאָּחיְי נ-a relaxed/satisfied spirit”, which is the aspect of Shabbos.
