They did nothing to earn it. Other powers will want it to and will have more pull to get it. Indeed, the Batavian Republic will probably be disestablished and replaced by the Kingdom of the Netherlands as IOTL (making Fulda free which probably as IOTL will fall to Hesse-Kassel), so that Kingdom will be not in any position to demand anything (again like IOTL, but there they gained the Southern Netherlands regardless as nobody wanted that land). One idea is, since Austria indeed doesnt actually want the Austrian Netherlands, to have the century old plan of Wittelsbach relocation going into effect now: Wittelsbach gains the west Rhenish territories including Austrian Netherlands (maybe excluding Cleves and Guelders going to Prussia), while Bavaria falls to Austria and Bavarian Franconia to Prussia. That works especially well if Bavaria continues to side with the French...
I really like this. Could we resurrect Lotharingia as the title of the new Austrian Netherlands-Rhinelands Kingdom? How would the culture difference between the Wallon and Flemish in former Austrian Netherlands and German Rhinelands work out?
Also, I assume that France gets left with 1789 borders, so they have the left bank of the Rhine- will the victors want to give the French-allied Wittelsbachs the right bank of the Rhine? I suppose the Wittelsbachs will have more motivation to be anti-French if they're next door- being the object of French territorial ambitions could have the effect.
If Lotharingia stays together, then could the Netherlands end up being swept up in a German unification? Lotharingia is going to have to be a part of a unified Germany, and the Netherlands would end up being surrounded by Germany. The Flemish population in the former Austrian Netherlands could end up seeing themselves as part of the German nation instead of developing their own nationalism- which could in turn influence the Netherlands to view themselves the same way.
Giving the Hapsburg more German territory is going to have some very, very serious knockon effects. The Kliendeutsch vs Grossdeutsch debate will certainly go a different way, with even more of the potential German nation under the Hapsburg's control. With more German territory, the Hapsburg might be willing to let go of their non-German territory in order to take the leadership of the Second Reich.
In OTL there were various schemes that were floated but never seriously pursued of splitting off different parts of the Hapsburg domain under cadet branches of the family. For instance Mexican Emperor Maximilian I was floated as a potential candidate for an Italian, Hungarian or Polish spin-off kingdom.
This could be pursued as a 19th century Hapsburg-wank. The Hapsburg, with more German territory, are willing to pursue a policy of greater German integration. Following the liberal revolutions in the mid-19th century the Kingdom of St. Stephen and Lombardy-Venetia are granted autonomy, with their own assemblies but with powerful, Vienna appointed Viceroys. This concession during the liberal revolution propels the Frankfurt Assembly to offer the Hapsburg Emperor the Imperial crown, with the caveat that the non-German territories must be made independent. The Hapsburg Emperor, having already granted autonomy to those territories, makes the leap and accepts the Imperial crown.
The Hapsburg now rule three different monarchies, the German Second Reich, the Kingdom of Lombardy (where the Lombard's Iron Crown has been resurrected), and the Kingdom of St. Stephen. The Hapsburg giant bestrides Europe like a collosus, from the Baltic to the Adriatic.
I might have gotten a little carried away.