I think you are unfair to Klenau. His previous record shows him as reasonably bold and competent, decidedly above the Austrian average. He is in a vulnerable position with an unfamiliar Corps he took control of *one* day before the battle. By 10am he was *well* in front of Kollowrat and he had only 14,000 men. He can't really advance toward the bridges without being disconnected from Kollowrat. Frankly I think that there are good odds if he had done that, that's the last we hear of his Corps. Same with a deep advance. More viable might be instead of having the bulk of his forces between Aspern and Breitlee, have it between Aspen and Essling and then advance straight north. It is a decent bit of space, so he is going to end up stalled by Massena south of Raasdorf. Still helpful, can throw some enfilading fire at the Grand Battery. Moral of the story though is he can and probably will do a lot more if Kollowrat is a few kms forward. And there is no reason that can't happen, why did it take until 9:30am to be fully lined up when the Grenadiers to the north did that at 7:30am and Klenau was advancing on Aspern at 8am.
In terms of how I see things going, sequential grinding up of the French center. This POD doesn't effect the other wing, so that still gets driven back. The problem for Napoleon is by the time it is clear he needs Davout/Oudinot, they will have advanced a decent ways and it will take several hours to get them to Raasdorf. He may end up unable to retreat to Lobau, but it is pretty unlikely that the army gets destroyed, instead retreat east once it gets dark. True they *think* Archduke John has 30,000 men, but they *know* Charles has 4X that. I think retreat toward Bratslavia, there is some rough terrain there, use it to anchor and cross. Charles also crosses somewhere. Then Napoleon has one last chance to win a great battle. The problem for Napoleon is he has less opportunity to pick up reenforcements, since Eugene left only ~8,000 men near Pressburg versus ~13,000 under Archduke John and ~25,000 Hungarian militia east of Pressburg admittedly of shaky quality. Napoleon may end up needing to retreat and that may well have to be toward Italy rather than Bavaria.
So what happens next? Serious, serious problems in Germany. With many of the Alpine passes blocked by insurgents, it is going to be an over 1,200km trip to get back to Southern Germany. Napoleon will transfer himself and likely cavalry before then, but it will be October by the time the infantry is back. Conveniently Austrian forces defeated a French Corps, the Westphalians, and Saxons west of Bohemia in the week after Wagram (only OTL to have their brilliant campaign be entirely pointless). I expect the Saxons flip quick, since Napoleon will be 0-for-2 and they are being occupied. There is less than 20,000 French in the Danubia (plus Bavarian, Wurttemburgian, and Baden although most of their forces were containing the Tyrol Rebellion). Once Archduke Charles connects with the Hungarians, he will be able to spend a few Corps west and I suspect at that point the South German states negotiate before they are occupied. Also, at the end of the month 40,000 British soldiers will land in Holland. Louis's relationship with Napoleon is rapidly deteriorating and he seemed to think his first loyalty was to his subjects, so I think he may well flip given Germany is collapsing, Napoleon is deep in Austria retreating toward Italy and he has a giant army on his doorstep. When Prussia and Russia join isn't *that* important since it will be several months before there will be a large French army on the German front (August/September for Prussia maybe? Since by that time other than some garrisons the French may be back on the Rhine, not sure for Russia but they weren't committed to Napoleon by any means and mopping up the Poles will be tempting).
It is quite possible for a Wagram victory to end similar to OTL just later. However, I think a scenario where Napoleon is facing a 1813 style coalition (perhaps a bit weaker, but then Napoleon is also missing the Confederation of the Rhine) by the end of the year is pretty plausible. It will be very different dynamic though. Unlike where it was 3 rough equals, Austria will be the clear senior partner with a much larger army than 1809. Russia is still early in reforming. Prussia will liberate itself but being returned to 1807 size will be more of a 'gift' of principle than 'earned'. It is also a different Austria in other ways, the peak of them leaning into Revolutionary Frenchness. Levee en mass, Austria's ~600,000 man army in 1809 would not be exceeded until Austria's mobilization in WWI. German nationalism, leaning into it.
Also, Napoleon being wounded is good. Him being killed might be a flop, end in a boring restoration of Peace of Amiens situation, everyone goes home. Need his reluctance to accept terms his opponents will take.
