Why would the Wettins gain control of Belgium and Westphalia? Belgium a rich, populous Flemish and Walloon province would not accept a German head of state. Trading Westphalia would remove any Prussian significance in West Germany, and as stated before would of been rewarding the Wettins for doing nothing, rather than a trade.
Assuming the Wettins only gain Prussian Rhineland (unincluding Westphalia and Belgium), you would see a significant change in German unification history. The first king of Saxony following the congress of Vienna was a staunch supporter of reforming Poland (in which he had a claim to). I could see in this timeline where he didn't have to manage a crumbling Saxony's economy and could instead focus on geopolitics with a Saxon-Rhineland, you could expect to see an anti-Prussian state form along Prussia's west.
I vaguely remember the person who suggested the concept of Trias being from Saxon/Bavarian origin, and the reason Trias failed was due to Bavaria not gaining enough support. Trias was the concept of a third German power out of the influence of the Austrian and Prussian circles, and would also be lead by Bavaria. With a better situated Wettin family that is now also anti-Prussian, they may be more keen in exploring this plan.
The Austro-Prussian war could of gone a lot differently with a stronger Wettin defensive, but assuming another Prussian victory you could see the abolition of the kingdom and it's incorporation into the North German confederation, and history would progress normally. However if Austria were to win the war somehow (possibly with a stronger Bavaria following a trias policy) I would assume either an annexation of Westphalia by Saxon-Rhineland, or the Saxon-Rhineland fall into the influence of a Bavarian lead South-German Confederation. The Austrians would also be a much more stable empire in this timeline, and be aligned with the SGC alienating Prussia causing a rebalance of powers in which you could see a Prussian British alliance reform.
Overall, I wouldn't expect the Lotharingia super-state your map had included, but either a more powerful Bavaria/a Bavarian lead coalition, or a medium-power to the west of Prussia following anti-Prussian ideologies, falling under spheres of influence of whoever would oppose the Prussians (French/Austrian/Bavarian,etc.)
I'm interested in how Saxon-Rhineland would interact with the British Hannover, but I don't know enough to predict anything about it.
EDIT: I'm also interested why you named this Kingdom 'Burgundy' when it includes zero Burgundian lands/connantations...