o this Elisabeth was not only a rich bohemian heiress but could she allow the Habsburgs to take Baden-Baden ( which was Catholic if I remember correctly) and unify it with the possessions of further Austria, correct ?
The Habsburgs could take the Bohemian lands, not so much Baden, which was to return to the Protestant Durlach line
but a Prussian / Hanover bride, and latter also means London ( and you run the same risk as Otl Anne of Hanover flop with Louis XV ) does not run the same problem of conversion, in Vienna she certainly cannot remain Lutheran, she will necessarily have to convert
The "flop" with Louis XV was a little more
nuanced than "she can't convert to Catholicism". Most of it had to do with the fact that she would be converting to Catholicism to marry the king of France. Her brother in Hannover had no children yet, and the 1718/1719 rising was in recent memory. That rising was driven by the Stuarts. Who had been
sheltered (until relatively recently)
by the king of France (yes, it was Louis XIV, but there were still enough Jacobites hanging around in Paris, plus, Louis XV's parents had been
pretty darn tight with James III. Yes, Louis was too young, but never can be too careful).
So, in sum, if the unthinkable had happened and
both the prince of Wales and duke of Cumberland died without issue, the king of France was married to the heiress to England. Yes, the Act of Settlement excluded any Catholics, but it is still a piece of paper (which doesn't really hold up well when there's a French army landing at Dover).
Walpole, Stanhope and the Dowager Duchess of Marlborough all wrote about this in their letters. Less that they minded her converting to marry than they were doubtful of how effective a measly slip of paper would be to "safeguard British liberties". Had Louis XV played for a younger daughter (Caroline or Amelia), in all likelihood they'd have accepted.
That being said: Karl VI was on George I's side
against the Stuarts (he'd forbidden James III from settling in the Low Countries - as originally planned - IIRC), he'd made a admittedly half-hearted attempt to stop Klementyna Sobieska from travelling to Italy (only reason he didn't was because of Captain Wogan and because Karl actually didn't see it as his "business" to get involved in what he viewed as a private squabble between George and James). And Karl VI turned down a suggestion (in the 1720s and again in the 1730s) of a potential match between Bonnie Prince Charlie and his youngest daughter, Maria Amalia (the 1720s proposal) or Maria Anna (in the 1730s) for fear of the offense it would give Britain.
Now...Karl VI didn't do this all out of the goodness of his heart. He wanted British support for the Pragmatic Sanction (among other things). And he had absolutely
no reason to
like the British (plus, the British wouldn't have the Pragmatic Sanction to hold over his head to force him to disband the Ostend Company- which, in its brief existence, effectively tanked the British tea/China trade monopoly*). Plus he blamed them as being the reason he lost the throne of Spain. So...Britain needs to resort to other weapons of diplomacy: marriage. Make a condition of the marriage contract that Karl either needs to disband the company or (at least) fire the Jacobites involved. Problem with disbanding the company is that there were a couple of high placed investors (including Prince Eugen of Savoie and Archduchess Maria Anna, the Queen of Portugal**) involved who objected. As seen by the fact that they tried to restart the Ostend Company several times after its closure.
*the main reason that the British
actually wanted the company closed had
less to do with the fact that it was screwing them over financially (when Jenkin's Ear was over, they picked up again) and more because the men at the levers of the company were exiled Jacobites- think the manager's name was Alexander Hume? but don't quote me- and that money was being funnelled back into England (through Ireland) to support the Jacobite movement.
**the company had a rather multinational aspect: Scottish bankers, Dutch sailors/ships and Portuguese merchants, at least half the investors also sat on the Privy Council in Vienna and the other half was from the Belgic aristocracy/burghers