In all seriousness, I think these two have enough in common where not much would really change during the Prequel years. Whether Teridax keeps his powers or not, he’s smart enough to pull off Palpatine’s plan pretty effectively - though perhaps in a more convoluted way, given his style.
Things might get more interesting later, though, as a result of Teridax’s disdain for powerful subordinates - I don’t think he’d have trusted Vader for very long (or tried to turn Luke to the Dark Side), instead simply ruling the empire more autonomously. This means that he might have actually succeeded in stopping the rebellion. And, also, he’s vain - his face would be everywhere. 
Death Star probably won’t exist in this timeline. While Palpatine has a few trusted allies and then destroys all the weaklings who oppose him, Teridax has no allies and prefers to subjugate and flex his power over anyone beneath him. He doesn’t just want power, he wants admiration - the only people he’d try and get rid of are those who are really likely to cause serious threat, or if his wants to make an example to a very specific audience (think Archives Massacre). I feel like the Death Star is too “blunt” an instrument for him to really want to have built.
Real question is whether he would consider the Star Wars galaxy worth ruling, or if he’d try to make his way back to the MU somehow. And that’s anyone’s guess. I don’t think he’d be too happy with the idea of a frail, time-limited body, however long it might live - remember that was how he used to keep his experiments under control.
These are just scattered thoughts - they apply mostly to round 1 and 2 (if he ends up having no knowledge or powers, he’d have to tread carefully. Otherwise he’s fine.)
The Bonus Round introduces an interesting element, because he’d probably want to find of some way to dispose of the Brotherhood all at once - they’d pose more threat to him than most other entities in the SW universe. So maybe the Death Star would come into existence here - but not as a political weapon so much as a stand-in for the energy storms. I can’t think of much else in SW off-hand that would be able to effectively eliminate that many Makuta without risk.
[Rise of Skywalker spoiler]
Also, Rey probably won’t exist.
