Is the Mirror Universe in Enterprise, Discovery, TOS and TNG (The Terran Empire) the same Mirror universe that is in Deep Space Nine?
If it is the same Mirror Universe what happened to the Terran Empire that turned the tables so completely and made Humans slaves to the Klingon/Romulan/Cardassian Empire?
Though it's possible there are at least two.
The first is the one we initially visit in "Mirror, Mirror", which is clearly the same one we later visit in Deep Space Nine; the DS9 episode "Crossover" has Intendant Kira mention the events of "Mirror, Mirror" as a matter of historical record:
Intendant: On my side, Kirk is one the most famous names in our history. Almost a century ago, a Terran starship Captain named James Kirk accidentally exchanged places with his counterpart from your side due to a transporter accident.
Deep Space Nine Season 2 Episode 23: "Crossover"
This episode marks the beginning of a multi-episode arc in the Mirror Universe, which continues to reference backward to past DS9 episodes1.
The second (which, again, may still be the same one) is the Mirror universe seen in Enterprise. The Enterprise episode "In a Mirror, Darkly" features the USS Defiant, originally from the original series episode "The Tholian Web" in a prominent role, but does not directly reference the universe seen in past shows.
That being the case, it was clearly the intention of the writers that this be the same universe; Mike Sussman, who wrote part one of "In a Mirror, Darkly", said in an interview at the time that:
["In a Mirror, Darkly" is] a prequel to 'Mirror, Mirror' and a sequel to 'The Tholian Web,' two of my favorite episodes
However, since there are no explicit references to other events known to occur in the Mirror universe, it's possible (though it seems unlikely) that this will be retconned. Regardless, we can be confident that the Mirror universe seen in Discovery is the same one seen in Enterprise: the USS Defiant from "In a Mirror, Darkly" is the primary plot driver of the Mirror-universe episode of Discovery.
Accidentally, of course. In "Crossover", Intendant Kira goes on to describe how Mirror-Spock took control of the Terran Empire and attempted to reform it from within. These reforms were remarkably successful, but ended up making the humans vulnerable to the Klingon-Cardassian alliance:
Intendant: While your Kirk was on this side, he met a Vulcan named Spock and somehow had a profound influence on him. Afterwards, Spock rose to Commander in Chief of the Empire by preaching reforms, disarmament, peace. It was quite a remarkable turnabout for his people. Unfortunately for them, when Spock had completed all these reforms, his empire was no longer in any position to defend itself against us.
Kira: Us?
Intendant: The Alliance. The historic coming together of the Klingons and the Cardassians.
Deep Space Nine Season 2 Episode 23: "Crossover"
1 Though there are some anachronisms that are easiest to explain by assuming multiple Mirror Universes; the DS9 episode "The Emperor's New Cloak" makes a plot point of how the Klingon-Cardassian Alliance lacks cloaking technology, despite Alliance ships being seen de-cloaking in the earlier episode "Through the Looking Glass." However, since it appears to keep continuity with the earlier episodes (the deaths of Mirror-Quark and Mirror-Rom, for example), we're a little stuck here. This is probably one of those things we shouldn't worry too much about.
