the "-stand" comes from the German word for "estate" in the medieval sense [1]. It's typically translated with small- and medium-sized enterprises, which is also the lingo used at EU level. As you said, it's a mass noun, so if you want to refer to an individual enterprise belonging to the "Mittelstand," you'd effectively use it as an adjective and speak of e.g. a Mittlestand firm.
How would you call a person belonging to the Mittelstand in German? In another Germanic language, Dutch, you would say "middenstander" (or plural"middenstanders"), derived from "middenstand".
Oh yeah, if we talk about a person, like the business owner or founder, I'd use Mittelständler and if I desperately tried to anglicize it to Mittelstander
[1]: https://en.wikipedia.org/wiki/Estates_of_the_realm