However, regarding Shabbos it says “and the layer of ‘Dew’ would go up”, and this happened during the day. Just like the physical dew evaporated and went up into the air during the day because of the heat of the sun, so too the spiritual idea that it represents is that Name of Havaya goes back up to its source on Shabbos due to an intense revelation of Hashem. This is the idea of “eat it (the Munn) today (on Shabbos)”, since Shabbos is especially connected to the idea of “day” and intense revelation, which affects the food that it not need spiritual refinement.
In addition, the connection between Shabbos and the Munn (that specifically on Shabbos they were commanded to eat it) is that the Munn is like the “dew”, it’s from the level of Hashem’s “Initiative from Above” which is from beyond the source of the creation of the world, and therefore came to everyone equally regardless of whether they were deserving. So too, on Shabbos there is a revelation from beyond Havaya, from the way that Havaya returns to its source in Hashem the way He is beyond the source of creation, from the level that is the source of the “Initiative from Above”.