Showing the soles of your feet to someone is extremely disrespectful in many middle eastern cultures including the Ottoman culture.
Nevertheless, I'm not sure if there is any reflection on the fact that mediterranean pirates (and nomadic tribes further east) plundered Balkans for captives and southwestern europeans then bought them. And that, perhaps, was a suboptimal way to behave.
As for why there's a "k" there - Greeks would naturally adapt any foreign word to the phonotactics of their language, which does not have "σλ" as a valid syllable onset, but does have "σκλ".
Sounds like there was to the Greeks:
Slav (n.) "one of the people who inhabit most of Eastern Europe," late 14c., Sclave, from Medieval Latin Sclavus (c. 800), from Byzantine Greek Sklabos (c. 580), from a shortening of Proto-Slavic sloveninu "a Slav"* -- https://www.etymonline.com/word/Slav
How is it not?
One of your other comments sounds like you agree with the etymology jefftk cited? But that says the exact same thing. The word slav was first, and the word slave was made from it.
Something being "propaganda" and "revenge" does not stop it from being the origin of a word.
Edit:
Oh, you elaborated slightly. > It's not derived, it's used - first by defeated.
That's what derived means. They took a word and used it to make a new word.