SETTE is not listed in W. Seibicke's Historisches Deutsches Vornamenbuch. This makes it rather unlikely that Sette is or was actually used as a registered given name.
Seibicke has SETTCHEN, though: pet form of
Lisette. And this makes sense to me and could well be the missing link to
Elisabeth. Of course
Lisette is a French variant of
Elisabeth, but the
German pronunciation lee-zeh-teh is possible and would lead to Sette (zeh-teh).
Roswitha as the origin of Sette seems very unlikely to me.