So I saw the chunks (from two different episodes) that have conversation about the Terran Empire.

In S3E5 (Die Trying), Georgiou and Dr Kovich are having a conversation and Kovich says “Unlike the Terran Empire which collapsed centuries ago. Were you aware that the distance between our two universes started expanding something after your departure? There hasn’t been a single crossing in over 500 years. You didn’t know that did you? You’re all alone now.”

In S3E9 (Terra Firma Part 1) the episode opens with a conversation between Kovich and Culber, talking about her symptoms. Kovich then talks about how LtCmdr Yor had come across from another alternate universe, the one from the Kelvin timeline movies, and forward. That fucked him up. He says that every molecule fights to either go back in time or jump a cosmic divide. Then “900 years have passed. The Prime and Mirror universes have been drifting apart the whole time.”

There’s nothing else that I saw about it. That being said, the conclusion you came to does make sense and I see how you got there.