What other German state can stay separate from a united Germany?
Every single one, as it is very much possible Germany would never unite.
Besides that there are the obvious ones like Luxemburg and Lichtenstein, who are like Austria not part of Germany and if you want to stretch the definition of Germany there are Belgium, the Netherlands, Switserland and even Lorraine, the Alsace, Burgundy and the Chech Republic.
Other German states would be state like Brandenburg-Prussia. They could easily form their own national identity, assuming they don't get any territories in the western part of Germany.
I would say that Hannover is a likely candidate, if the personal union with Britain continues. It stays out of the unification wars and ends up outside Germany and creates its own national identity in the 19th and 20th century.
Another good candidate would be Schliswich-Holstein. They could easily end up Danish instead of German.
Bavaria still has its own strong regional identity. I can see that developing in its own national identy.
So there are large parts that could remain outside of Germany, assuming Germany actualy forms.
BTW I assume a potentiol POD before the (mid) 19th century. The closer you come to 1870 the likelier it becomes OTL Germany forms