One of the songs that is sung Friday night is Koh Ribon. There is not a single mention of Shabbos in it. Why do we sing it on Shabbos?
It speaks of the created world and praising HaShem for it i.e. G-d the Master of all Worlds, You are the Ruler, above all rulers. Your mighty deeds and wonders, it is beautiful to declare before You. I will sing Your praises in the morning and the evenings, to You Holy G-d Who created every soul, the angels above, all people, and the beasts that roam the grounds and the birds of the sky. Translation from here where there is a catchy recording.
There is not a single mention of Shabbos in Koh Ribon...
...or Tzur Mishelo, or Kel Adon, or the special Kedushas on Shabbat morning, or the extra psalms in P'sukei D'zimra, or the deluxe version of taking out the Torah.
Shabbos is just a very special day! It has the special mitzvot of Kavod and Oneg. Not everything has to announce its connection to Shabbos. Just spending a little more time eating, davening, and singing is also an honor and a pleasure.
What is Shabbat if not the proclamation that Gd is the Master of the world?
I'm gonna just guess - Zecher LeMa'aseh Bereishith/Zecher LiYtziath Mitzrayim. Sorry I don't have the freedom to look up sources on this at work.