Now the topic of something akin to the clone wars happening with or without ol' papa Sheev I've already seen done to death by now. We all know a civil war was bound to happen due to how corrupt the Republic had gotten by that point, But I wanna go a step further and say the Empire itself was always gonna happen. Would it have been CALLED the empire? maybe, maybe not, but by all intents and purposes, the galaxy would have gotten something like this even if the name was different (minus all the sith nonsense ofc).
To properly explain my logic, ima go through the specific processes on how this would have gone if Palpatine either never existed, never rose to power, whatever;

-A civil war between primarily the core worlds, and the outer rim breaks out. There would not be clones fighting for the republic, and there would PROBABLY not be battle droids fighting for the seperatists, but a war happens nonetheless.

-The republic forces (in this hypothetical timeline, they would be conscripts most likely) wouldn't have clone armor itself, however we must remember; clone armor, due to it's shared design-inspiration, is very similar in appearance to the armor worn by troopers during the age of the Old Republic. Its safe to assume that as the republic re-arms for war, the designs they use for their new gear would be inspired by old republic armor (why re-design something from scratch when you can just improve upon what already exists?). And the end result would be that these non-clone republic troopers would be wearing something very similar in appearance to the clone trooper armor we actually got.
Now what does this have to do with the Empire? Well as we all know; Stormtrooper armor is based on / an evolution of Phase II clone armor. Palpatine may have pushed through the change from clone to stormtrooper, but the armor evolution was always planned to happen either way. So again; the end result here would be that when this alternate empire rises to power, we would see maybe not a 1-to-1 copy of stormtroopers and their armor, but something VERY similar.

-shorter explanation this time, but it's the same story with the vehicles; Kuat Drive Yards, and by extension; Rothana Heavy Engineering, have always been the republics primary manufacture of wartime ships and vehicles. And it's not like the stuff they made for the clone wars was hyper-sepcialized specifically for clones or anything. So really, we would have almost certainly seen just straight-up Venators, AT-TEs, LaaTs etc. And as we know; the designs for those vehicles were the direct insparation for things like imperial-class Star Destroyers and At-Ats.

-Now for the political side of thing. The Republic would almost certainly win this war. Without any sith tom-foolery, the likelyhood that the seperatists wouldn't have their battle droids in this timeline, and the near-guarentee that the Republic would have the corperate backing in this secenario, yeah the CIS has no chance. But why does this lead to the empire? Well authoritarian regimes rising to power after a state of chaos or war, because the people crave security and saftey is something we've seen plenty of times (both in works of fiction, and irl). And remember; the majority of the senate cheered when Palpatine crowned himself emperor. This was something they were on-board with, and even without Palpatine, it probably would have happened. Again, we may not get the Empire itself, it may just be a more authoritarian Republic. But aside from that, we would basically have a pre-'A new hope' Empire in everything but name; Complete with the Imperial Senate and all-that.

-And finally, what happens to the Jedi in this scenario? Well that's hard to say, but the main deciding factor would be which side they chose to back in the war. Either way, I imagine the Jedi would pack up and leave Coruscant, as the new regime probably wouldn't sit right with most of them, However if the Jedi fought in the war on the side of the Republic, like in the main timeline, then I could see some Jedi breaking off from the order to fully work with the Empire, either due to true loyalty and belief in the new system, or simply because they've already invested so much in it during the war. The rest though? idk they'd probably return to Tython or something. But if the Jedi sided with the CIS in this timeline? that's a whole different story. Obviously they wouldn't be on Coruscant anymore, and I could see this alternate Empire / Republic outlawing their religion due to the war. I don't think there would be a full-on Jedi purge, but the order would most-certainly NOT be on good terms with the new order.

Anyway, that's my little shower-thought rant about an empire without Palpatine, hope y'all enjoyed!