A new update for Skyrim Anniversary Edition fixes an issue with black screens.
Unfortunately it also breaks mods. What's more, because the recently released Anniversary Edition is actually an upgrade to the previously released Special Edition, the update will affect owners of either version.
Players had reported an issue with the game where the screen would show black with the music still playing.
Modders discovered that the latest build of Skyrim runs scripts faster than previous ones did, causing an issue with mods.
This new update fixes the problem. However, new Skyrim patches bring compatibility issues for mods until updated to the latest version.
And, as previously reported, this causes problems with the Skyrim Script Extender plug-in that's used for mods.
Until the Script Extender is updated, players will likely have problems playing the game with mods enabled.
In the meantime, it's possible to load the game through the Script Extender with "don't update automatically" selected. Or you can revert back to an older version of the game - there's a mod for that, of course.