Samstag is only *one* German word for Saturday. It is used in southern and western Germany and has become the more general word you would always hear in the news. But in the rest of Germany "Sonnabend" is more common, indicating the day (literally "eve") before Sunday. "Sonntag" was adapted by most Germanic tribes from Latin "dies solis" before the 4th cent. i.e. before the beginning of Christianization.
Now the connection between Hebrew "shabbat" and German "Samstag" has nothing to do with Yiddish. It was the church that brought the Greek "sabbaton" or Latin "sabbatum" (originally “sabbata”, f.) to the Teutons. I have no idea what name was they used before that (I suppose, they had a name taken from Saturn like in English), but I believe that it was the biblical use of “sabbatum”, that helped it make its way. In the bible “shabbat” or “sabbaton” is the only day with a specific name, the others were just given numbers.
I read, it was the Gothic (Arian) missionaries, who brought the “Samstag” to the south of Germany, shipping up the Donau. The Gothic word for it was “sambato”, hence the M in SaMstag, but this again is from vulgar Greek “sambaton”.
Now to “Sonnabend”. This came to Germany with the Anglo-Saxon missionaries (7./8. cent.?). Old English “sunnanaefen” became “sunnunaband” and originally meant only Saturday evening, but was later extended to the whole day and thus superseded the old expression. This again was a name that had Saturn in it, because you will still find vernacular “Satertag” or “Saterstag” in some areas in the north west of Germany.
I’d really be interested in learning more about the days of the week in other languages. Also please correct me with what I’ve written above, because I had to collect the information from various books, far from being an expert.