It must be nice to be able to commit to a regular sleep schedule.

It was kind of talked about on Discovery with Georgiou after they went to the future. The universes were drifting apart, and because the mirror universe was no longer aligned with the primer universe in whatever year Discovery ended up in, Georgiou was not able to maintain cohesion and had to go back in time. link

I may be misremembering headcannon as an actual line from the episode but I seem to remember hearing that the mirror universe was the one that was the closest to them on the space time continuum. The fact that they were both aligned is why people could travel between them and not others.

They are extremely similar so presumably the barriers between the two are thin.

That's something they've said, but it doesn't make much sense. Most of the universes Worf went to in that episode are much more like the Prime one than the Mirror Universe is.