In Hebrew the words share two of the three letters of the root:
Sabbath (Shabbat), שַׁבָּת, is Strong's H7676. It is spelled shin-bet-taf.
Seven, שֶׁבַע, is Strong's H7651. It is spelled shin-bet-'ayin.
While Shabbat does fall on the seventh day of the week, Strong's doesn't note a linguistic connection between the two words nor have I ever learned one (for what that's worth). As far as I can tell they are just two similar-looking words.
It appears from a cursory inspection of tractate Shabbat in the Babylonian talmud that Aramaic uses the same roots for these words. (This is as expected, but I did my best to verify. My Aramaic is weaker than my Hebrew.)
I do not know about Greek.
Please note: This answer was written for a neutral, academic audience
and is not intended to be interpreted in the context of a religious
belief or doctrine.