"Suped-up": is it a real idiom (vs souped-up)

Both sources below attest that the correct more common spelling is soup-up. Suped-up and sooped-up are are just misspellings. The expression is AmE in origin and it most likely derives from supercharge:

As World Wide Words notes:

Souped-up is known both in the UK and the US and was actually created in the latter country. It’s one of the longer-lived slang terms, still widely used. In its first sense, in the 1920s, souped-up specifically meant to modify a motor vehicle to increase its power and efficiency.

The earliest example I can find is this:

• Speedster, classy, souped up ... $125. A newspaper advertisement by a Ford dealer in the Oakland Tribune of California, 21 Sep. 1924.

Souped-up must at root derive from super, as in supercharger. This term for a device to increase the pressure of the fuel-air mixture in an engine to improve its performance is known from 1919........ However, there’s almost certainly a connection with the foodstuff, which would account for the shift in spelling.

Soup has at times been a slang term applied to several murky liquids. If you’re a fan of American detective stories, you may know soup as a term for the nitroglycerine that was employed in safe-cracking, a slang term widely used in newspaper reports of criminal activity from about 1900 onwards (it was called soup because it was extracted from dynamite by immersing the sticks in boiling water). And it was recorded in Webster’s Dictionary in 1911 that soup was “any material injected into a horse with a view to changing its speed or temperament”.

It seems that supercharger combined with the racing and criminal senses of soup to make souped-up.

And from The Grammarist

Soup up is the phrasal verb meaning to modify something to increase its power, efficiency, or impressiveness. Soop up is a common misspelling, and supe up is a less common one (both soop and supe have rare senses that have nothing to do with increasing power or efficiency).

Soup up originated in the U.S. in the late 19th century, though it wasn’t widely used until the 20th century. Its exact origins are unknown, but it could be short for supercharge, or it might come from a horse-racing slang term for injecting horses with narcotics meant to make them run faster.1 Through the middle decades of the 20th century, it usually applied to engines, but today souped up is used in all sorts of contexts.