Fundamentally, we are not an empire - we are a republic. Feel like that has gotten lost in the noise recently.

Name some examples.

Byzantine Empire? Lasted over a thousand years, fell to the Ottoman cannons.

By the time the Ottomans took Constantinople, the Byzantine Empire had been in decline for centuries already. The crusaders and Venetians took Constantinople 200 years previously, and while the Byzantines eventually recaptured it, that was still an ultimately fatal blow. And even that blow was only possible because Venice had been allowed to drift out of the Byzantine sphere of influence.

I immediately regretted my claim soon after posting it, and this was the first example I had in mind, along with this counterargument. If I was to make a further (somewhat weak) counter-argument, it was engineering know-how that established the Roman Empire as a dominant military in the first place, consuming the territories of other empires. It's a safer claim that technological asymmetry permitted the conquest of the less equipped 'societies', rather than 'empires'.

I agree with you - but there are counter examples.

Germany made some amazing developments that were superior to allied tech, and they didn’t win.

This is almost entirely a myth. If you set aside all of the fantastical prototypes, there are a few plausible examples but none that are truly “amazing”. For example, Germany did develop some of the earliest jet engines, but then again, so did Britain. The Me 262 and Gloster Meteor were introduced within months of each other, and while the Messerschmidt had its advantages, it also required scarce materials and couldn’t be manufactured at scale. Manufacturing issues were also present with the later German tanks, which were also significantly less maintainable and less reliable than Allied tanks.

One place where they were significantly ahead was in large scale rocketry. By the same token, they were significantly and consistently behind the United Kingdom and United States in cryptography, computing, radar, electronics, atomics, and manufacturing—all of which had much more significant strategic impacts.

the Spanish using guns and horses to topple the Aztec empire? and smallpox, but the guns and horses helped.

The Aztecs were toppled because they had alienated all of their neighbors and vassal states. The main thing the Spanish did was to organize everyone against the Aztecs. They had guns and horses, sure, but not nearly enough to singlehandedly make a difference on the battlefield.