Bethesda is working on a patch for the Skyrim Anniversary Edition update
But "it's taking a little longer than we'd like".
Skyrim Anniversary Edition came out a week ago, and with it Skyrim Special Edition updated to version 1.6. While Bethesda worked with the Skyrim Script Extender's developers to prevent the update from being too disruptive of the RPG's more ambitious mods, the update has caused a black-screen bug on loading saves, which is even affecting players who don't use mods. (Apparently, completing the Civil War questline consistently sets it off.)
There's also been a general increase in freezes, infinite loading screens, and PlayStation users are reporting the return of an old glitch that tells them they need to free up "0 kb on the system storage" to play. (Here's a post about it from two years ago—it's apparently caused by Creation Club content.)
On Discord, Bethesda has said, "We are aware of the 0kb error some PS4 players are experiencing as well as the 'black screen' issue. The team has been working on a fix for these (it's taking a little longer than we'd like) and hopes to have them resolved as soon as we can." A patch is in the works, and should be ready "early next week".
In the meantime, modders have come to the rescue. There's a rollback mod for reverting to version 1.5.97 and work has resumed on EngineFixesSkyrim64, with a version for the Anniversary Edition currently in beta.