The release of Skyrim Anniversary Edition proved to be less disruptive than many had expected, especially for the modding community who were pleased to learn that the Skyrim Script Extender team had early access to ensure that mods would still be compatible after the update.
The bad news is there was one nasty bug introduced in the update, which causes a black screen on loading save games, allegedly once the Civil War questline has been completed. There's a number of other bugs reported too, such as loading screen crashes and PlayStation specific issues relating to system storage.
The good news is that Bethesda has promised that a fix is coming, posting on Discord to state that "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."
The new patch should hopefully launch next week, but in the meantime, there's a rollback mod that will bring the game back to the pre-Anniversary edition version, if you don't mind tinkering.