Hmm, the possiblity of a Prussian Bohemia raises a lt of question pertaining potential butterflies.
First, let's take into consideration the distribution of economic development within A-H: True capitalistic industrial modernization only really gained momentum in the empie AFTER the formation of the Dual Monarchy, with economic growth being focused around the Austrian and Bohemian crownlands, as well as the recently booming Hungarian city of Pest, the commercial, political and cultural center of Transleithania, wich was merged with the old capitals of Buda and Obuda to form Budapest. Only by the end of the 19th century did this trend began to expand into the Hungarian Plain and Carpathean region, while the easternmost regions were an important source of grain and, in the case of galicia, oil (in the early 20th century, mostly). So, in the short term, the balance of (economic) power in the still pseudo-medieval Habsburg empire will start to lean to the Hungarian side, which will make it even easier for them to press the emperor into a Dual Monarchy, as I too don't believe they would push for full indepedence if they feel they can have the upper hand in the relationship.
Second, there's the military drawback of losing Bohemia, from where a disproportionally large part of the Austrian army was recruited, and represented around 15 % of the population of Cisleithania (Austrian side). So this means that the army will either never be the same, or will come to depend heavily on some other province (maybe Transylvania), which would further diminish Austrian power in the DM and, maybe more importantly, might make them less able to defend their posessions than they were IOTL. Im particularly thinking of a future attempt by Italy to claim Trentino and Trieste, as in this scenario a Hungarian dominated military may be less determined to fight for Austrian territories full of noisy italians and slavs. As a side note, under Prussian military command Bohemia might be even more of a valuable asset than it was to Habsburg military, which might have an effect in the Franco-Prussian war.
In the middle to long term however, I'm a bit exceptical about the survival of this alternate A-H. Assuming it doesnt get butchered in another war (which I think might just be the most likely scenario, but more on that in next post), as long as industrialization progresses like IOTL, the power balance will become way too... balanced. Part of what kept the mess that was A-H intact was that the Austrians had the clear upperhand, and thats a position that mostly rural Hungary is unlikely to be able to mantain. An equal power distribution will lead to even more friction with the Magyar nobility, and as a consequence the empire runs the risk of becoming increasingly divided due to unability to get things done.
I'll talk about how this could affect Prussia and the other continental european countries in anothe post, but I hope this gives some food for thought. Also, something to this effect has been discussed before:
https://www.alternatehistory.com/forum/threads/pc-prussia-presses-on-after-königgrätz.386490/ Its basically about what happens if Prussia presses on after the Battle of Konningratz, which is probably what would be necessary to do in order to get FJ to accept this terms.
PS: This is my first post, so I REALLY hope it doesnt get buried T_T