Well I think a hypothetical Galicia like that would actually be sovereign and independent. And so would a potential Poland. The German republic would have no interest and claim on Galicia as Galician. BUT it would have a self-interest in supporting the creation of states politically and ideologically aligned with itself.
My understanding of the Frankfurt Assembly is that it was based on a constitutional monarchy. I would favor having Prussia, Hanover, Saxony, Württemberg and Austria as as royal members of the federation and the Austrian emperor as the head of state and king of Austria. He could also remain as King of Hungary cementing that alliance. However all monarchs would reign but would not rule. Each state would have its own parliament. Going directly to a republic means the Head of State would be elected and that office should be apolitical.