I just dont see it really, i doubt any of the other would have let Prussia seize all of Bohemia in 1866.
I think you underestimate how big a change the
OTL Austro-Prussian War was, to the balance of power as it previously existed.
With retrospect it's easy to say "Oh, Prussia became dominant in Germany", as if that's a negligible thing, or as if that's an expected thing. It wasn't. Prussia tore apart the German Confederation that was created at the Congress of Vienna, humiliated the hitherto-greatest of the Central European powers, annexed vast swathes of German land—including the Kingdom of Hanover, which had a strong blood relation to the British Crown—and puppeted most of the rest of Germany, excluding only Hesse-Darmstadt, Bavaria, Württemburg and Baden…
…and the Prussians got away with it happily. The other great powers didn't intervene. And that's in the circumstance when the Prussians started the war, against all the other German Confederation states, by invading territory held by the rest of the German Confederation. Prussia was clearly the aggressor. OTL Prussia's actions were more threatening than TTL Austria's actions. Yet no-one intervened against Prussia in OTL.
I agree with you that the Austrians retaking Silesia is vaguely comparable to the idea of the Prussians taking Bohemia, in terms of how big a change it is to the balance of power. But compared with the huge deal of the Prussians actually did do—bringing most of Germany under their dominion and tearing apart the post-Napoleonic-Wars settlement in Central Europe—the Prussians "merely" annexing Bohemia would have been small by comparison. This change is a
less radical change to the balance of power than what the Prussians did in OTL. And the OTL Prussians got away with it.
No way Russia allows anything like an independent Poland to appear, even if it's an obvious Habsburg puppet compared of discontinuous parts, as this might give the denizens of Congress Poland the wrong ideas.
I agree with this bit.
However, I don't agree that the other great powers would intervene to help Prussia. I'm pretty convinced that Austria could get away with retaking Silesia (otherwise I wouldn't have put that in the premise). And Austria is in charge here, not Saxony. Maybe Saxony would gain territory at Prussia's expense, yes that's believable; but the Austrian Empire is in the driving seat here. If the Austrian-German armies have done well enough in the war to award Prussia's Saxon province back to Saxony, I don't think they would be so selfless as to help Saxony but not retake Silesia for themselves.
If people are utterly unconvinced, maybe we need Napoleon III to be more involved in his OTL North American misadventures, so that he's even more distracted than he was in OTL. That would help make other-great-power intervention less likely.