Prussia is largely an insignificant state at this time, or at least considered to be so. It was them seizing Silesia that put them on the global scene. We know, with the benefit of hind sight, how terrifying a Habsburg-Hohenzollern Union would be, however at the time this wasn't yet understood.
As for the other states potentially opposing the union, let's look at them one by one;
France : Already opposed Maria Theresa coming to the throne of Austria no matter who her husband was. Historically their performance in the war of Austrian Succession was largely on the crap side of mixed, with early successes in Bohemia giving way to disaster in Bavaria, and only a few successes at the end in the Netherlands, for which they received nothing. Without Prussia distracting Austria they will be the primary target, and with Prussian support I expect they'll get their ass kicked.
Russia : I remain skeptical that they would care. They supported Austria in the war historically, and had been long time allies in the War of Polish Succession and the wars against the Turks. I doubt they will oppose the union. What would be more likely is them demanding aid against the Turks and recognition of Russian expansion into the Balkans in exchange for Russian recognition of the Union.
Britain : Will probably not see this union as a threat initially, primarily because of the perceived weakness of Prussia and because Austria is not a Naval Power, and neither is Prussia,. They will be more worried about France getting the Southern Netherlands. With Prussian successes during the war this may change, but I doubt it would be enough to make Britain officially oppose the union.
Sweden : Is currently getting their hesitating ass handed to them in
The Hat's War. Even if they weren't, the Golden Age of Sweden has long since passed. Their historical record for wars in this time period was one of consistently getting their face smashed in and losing all of their past gains, primarily to Russia, but also their gains in Pomerania to Prussia.
Denmark : Has been consistently either Neutral or on Austria's side ever since the Habsburgs wrecked their shit during the 30 Years War primarily due to their rivalry with Sweden. Prussia is currently one of Sweden's competitors, having seized parts of Pomerania in the Great Northern War. Denmark likely sits this one out unless Sweden joins, in which case if Denmark joins they likely join against them. In all honesty, if Sweden joins against Austria-Prussia that's probably going to just secure the aid of Russia and Denmark for the Union since the two will love this opportunity to kick Sweden while they are distracted.
Spain : Already opposed to Austria with the goal of conquering Austria's Northern Italian Territories. That's not going to change, and neither will their performance. Historically they secured a decent amount of territory in the form of client states. But with Prussian Support Austria has more resources to shift south. That said I expect Austria will focus more strongly on France if given the opportunity, so Spain likely still comes out with some gains.
Sardinia-Piedmont : Supported Austria, while demanding concessions, because Austria was far less of a threat than what was on the verge of becoming complete Bourbon Encirclement. That's not going to change here. Spain will still be marching north, trying to get Milan. Sardinia-Piedmont will want to prevent this from happening, and so will be on Austria's Side. The Bourbons are the immediate major threat, Austria-Prussia is a distant hypothetical that's generally been on their side.
The Netherlands : Much like Britain is far more worried, and with good cause since the only time this actually happened it gave way to near immediate annexation, about the possibility of a French Controlled Southern Netherlands than they are with Austria gaining the lands of a minor state on the Eastern end of the Holy Roman Empire. They won't oppose the union, they might stay neutral.
Hanover : Is tied to Britain and does whatever they want so Britain's evaluation applies here as well. Even if they were independent Hanover's performance in the wars of this time period generally boiled down to being quickly and easily occupied by whatever continental power was at war with Britain at the time unless Britain had the forces to bail them out or that power was focused elsewhere.
Saxony : Historically already did oppose Austria but didn't do much of anything and eventually went home out of boredom before switching sides where they provided basically nothing to the point that Freddy Prince Junior had no problem just marching entire armies down through Saxony and decisively kicked the ass of Austria and Saxony when they linked up. They might be a bit more encouraged to fight off the union but again didn't really contribute much and with Prussia right next door supporting Austria, they're prospects don't look too good. If anything, I expect the diplomatic situation may secure their neutrality since they would be surrounded by Austria-Prussia and obviously screwed unless France goes up to defend them, which they almost assuredly won't.
Bavaria : Historically had the support of France and still got pounded into the dirt and spent most of the entire war completely occupied by Austria.
What other states are there? Is the Elector of Cologne gonna raise an army? Will Hesse-Darmstadt start yelling? Dear God, maybe Venice will mobilize their !!!4!!! War Galleys! I'm sure Maria and Freddy are quaking in their boots.
In the end, some states will oppose this. Plenty of others will still see this as the Lesser of Two Evils or even a definitive good. This isn't Europa Universalis where countries just cross an arbitrary badboy threshold and then everybody loses their minds. The states that are likely to oppose this already tried to kill Austria historically and Maria Theresa kicked their ass.
P.S.: I disagree with that timeline being well written, if its the one I'm thinking of, because from what I remember the author basically sidelined Maria Theresa to Wank the shit outta Freddy. You can't just shove one of the most talented and strong willed female monarchs in history into the kitchen, that shit aint gonna fly.