My first impression would be that The Dutch Republic would be better off than OTL. Many of the Dutch patriots active in the revolts fled to France after the Prussian invasion and returned later with the victorious French troops. But this liberation came with a heavy price tag. And the Republic was further drawn in the struggle against Great Britain. That was not really in the Interest of the Dutch, because colonial defenses proved to be largely inadequate. It showed how overextended the Dutch colonial empire was at that point in time.
I can see the victorious patriots of the ATL trying to implement the same necessary political reforms: That means centralisation of government, an increase of the political influence of groups that were excluded in the period before the 1780's and as a consequence the legal equality of the different religions, the removal of the last economical remnants of feudalism. Also a further liberalization of the written word.
If the New 'trully Liberated and United Dutch Republic' can somehow defend itself against the initially hostile Prussians* (And to be honest, those early Dutch militia didn't have a change against the professionals of the Prussian Army) it's foreign policy will turn more and more towards France, with or without French revolution. The patriots overestimated the militairy strenght of the republic. The dissastrous defeats of the fleet in the war of 1780-1784 were explained by the incompetence and corruption of the stadtholder and the ruling elites, but at the same time it had been the patriots who initially were hawkish and drove the Republic to war with England. Willem V never wanted war. So i think a succesfull Dutch revolt wil have a hostile policy towards Great Britain, and may be easy drawn into a new war, that may again end badly for the Dutch.
A question is if like the French Revolution, the Dutch revolt will radicalize. I don't have the definite answer there, but i believe some crucial elements are missing in the Dutch Republic . In OTL the Batavian Republic never really radicalized, but it must be said that as it was founded at the end of the Terror of the French Revolution, the experience of the patriot refugees in France may have been a lesson for them, which way not to go. The main political issue in the batavian republic was the practical issue of centralisation, not so much ideological issues. That issue of centralisation was responsible for a couple of coups in the batavian republic, but several of them were initiated by the French 'overlords' to get better control. In the ATL there will probably no French occupation, i'm not sure if this makes the Liberated and United Republic more stable or the reverse.
*As stadtholder Willem V was maried to Wilhelmina of Prussia, this is hard to avoid.