I can confirm that in Hebrew, the name for Sunday translates into "First Day", Monday into "Second Day", etc. Except for Saturday, which is Shabat.
Klein Dictionary gives the etymology of שַׁבָּת as derived from שׁבת (to rest). I also found references suggesting the origin is with the Akkadian šapattum, the 15th of the month, but none related to שׁבע (which originates in Proto-Canaanite).
היּוֹם הַשְּׁבִיעִי (note the definite form!) is how Saturday is referred to in Genesis 2:2-3, without actually having the name שַׁבָּת. There's a some discussion about why שַׁבָּת isn't mentioned there as a name for the day, but regardless, your comment is the first time I read of the etymology of שַׁבָּת deriving from שׁבע.
> Other related words are ... to sheva (שֶׁבַע) meaning seven, as Shabbat is the seventh day of the week ...
¹ “Fair” as in “a gathering of stalls and amusements for public entertainment”.