What is the historical origin of the Jewish Sabbath?

I think we can have an answer based on the two comments by @MarkC.Wallace and @Spencer under the question, linking to

• The Mysterious Origins of the Sabbath on ReformJudaism.org, and

• Wikipedia article on the history of the week.

Let’s take a look at some passages of the first article:

In ancient Babylonia, the Akkadian word shab/pattum corresponded to the fifteenth day of the month as a day of quieting god’s heart. There are those who maintain that it comes from another Akkadian word, sebutum, meaning the seventh day…

It is also not clear how the noun Shabbat was originally connected to the verb shavat, meaning “to rest,” or if one was actually derived from the other.

All ancient facts are more or less mysterious, but as expected there is a clear pre-Jewish Summerian-Akkadian (Mesopotamian) connection.

Looking at Wikipedia article:

The earliest evidence of an astrological significance of a seven-day period is connected to Gudea, the priest-king of Lagash in Summer during the Gutian dynasty, who built a seven-room temple, which he dedicated with a seven-day festival. In the flood story of the Assyro-Babylonian Epic of Gilgamesh, the storm lasts for seven days, the dove is sent out after seven days, and the Noah-like character of Utnapishtim leaves the ark seven days after it reaches the firm ground.

Counting from the new moon, the Babylonians celebrated the 7th, 14th, 21st and 28th as "holy-days", also called "evil days" (meaning "unsuitable" for prohibited activities). On these days, officials were prohibited from various activities and common men were forbidden to "make a wish", and at least the 28th was known as a "rest-day". On each of them, offerings were made to a different god and goddess. In a frequently-quoted suggestion going back to the early 20th century,the Hebrew Sabbath is compared to the Sumerian sa-bat "mid-rest", a term for the full moon. The Sumerian term has been reconstructed as rendered Sapattum or Sabattum in Babylonian... It is possible that the Hebrew seven-day week is based on the Babylonian tradition, although going through certain adaptations.

As the question is whether a weekly day of rest and devotion is original to Judaism, or can its origins be traced back to a prior non-Jewish source, the answer is obvious.

• The seven-day cycle is an astronomical/astrological idea invented and developed by older civilizations of the Fertile Crescent that influenced the Canaan area (Summer, Akkad, Babilon).
• In that 7-day moon cycle, each 7th day was sacred, during which some actions were prohibited
• At least one in four of these sacred days was a day of rest
• The very name Sabbath can be traced back to Sumer

But on this background Jewish/Biblical interpretations can be seen as innovative:

• The astrologically-centered moon-cyclic meaning is replaced in the Bible with a perspective centered on the monotheistic principle.
• Judaism promoted a moral discriminatory idea of the sacred itself: the sacred day ceases to be both “holy” and “evil”.

Some older Western historiography was inclined (especially in the protestant Anglo-Saxon world) to look for absolute originality of all things Jewish. Until recently there was even a “Biblical archaeology” trend of simply “proving” the Bible literally true by unearthing what the Bible described. The recent and more scientific approach on the matter is to ask how and to what degree anything in the Middle East is related to the larger context created by the massive and important Sumerian and Egyptian cultures that preceded any others by millennia. On that background, looking for absolute innovations doesn’t make much sense, and any innovation can be related to some precedent, as a continuation and/or as a change. Most Jewish traditions are modifications (in some cases revolutionary reinterpretations) of previous elements. Taking into account their background is a prerequisite to understanding changes involved in these innovations.