So no war of 1870/71? Because the borders from Prussia are the result of 1866.
If you forbid any changes of the borders of Prussia towards Denmark, Russia (or Polish Russia, which could gain independence), Austria-Hungaria, the Netherlands, and Belgium, the result would be, that every kind of war on a large scale in central Europe is forbidden, or Prussia isn't allowed to participate in these wars, or Prussia isn't allowed to win or loose such a central European war.
The smaller principalities and Oldenburg, and Mecklenburg have no choice but to cooperate with Prussia. A formal annexation isn't even necessary for that. And the decision to form the "Norddeutschen Bund" (some kind of federation between Prussia and other states in northern Germany) was even 5 days before the peace treaty with Austria-Hungary. But by your challenge the "Norddeutscher Bund" could only become some kind of military alliance and confederation, and not a country, because this would perhaps change Prussia.
The principalities in Thuringia are to small to be relevant in any matter.
It would be interesting which side Bavaria, Baden and Würrtemberg choose. In OTL they had some secret treaties with Prussia.
If Austria-Hungary or France would try to annex parts of them, the result would be a war with Prussia, which is forbidden by your challenge, because a Prussian defeat would also change the borders of Prussia, and a victory of Prussia could lead to German Unification.
The "Zollverein" between Prussia and other German states (but without Austria-Hungary) would mean, that economic growth is still possible in Germany without the unification.
The greatest result would be the no devastation of central Europe because World Wars are impossible (in Central Europe) according to your challenge. Therefore the Age of Imperialism could remain longer (but not indefinitely) (because the Colonial Powers are perhaps not exhausted (like OTL because of the World Wars). In Central Europe many old buildings would survive, this would change the look of German cities compared to OTL.
Prussia is still powerful enough to gain some small colonies.
Stronger regional identities in Baden, Würrtemberg, Bavaria, Saxony, Hessen-Darmstadt are maybe the result.
Some form of constitutional monarchy is possible in the 2000ies in the German States, but if there is some form of crisis (economic, political) some of them could become republics.