Bethesda has a knack for releasing buggy games but also kicking in the shins anyone who attempts to fix them in an unofficial manner. It seems Skyrim Anniversary Edition will be the same.
Skyrim Anniversary Edition comes with a pile of mods right out of the proverbial box which could lead you into thinking the game will be more mod-friendly than anything so far. This might end up being a deceptive statement though as there are already concerns about how the game might mess up the existing mods.
The potential issues' severity prompted the developer of the Skyrim Script Extender (SKSE) to speak up on Reddit. The developer noted that the release of Anniversary Edition can end up with mods made with the native code underneath not working and they will remain broken for an unknown amount of time after the release.
This is pretty severe and it appears that all the mods using SKSE will get botched with the update, which is not that new - Bethesda has been consistently ruining mods' functionality, patch in, patch out.
Anyway, in order to circumvent the loss of your favourite mods in the collection, you might want to back them up somewhere and then make Skyrim Special Edition able to update itself only when launched. Once that's done, make sure you never, I repeat - never launch Skyrim Special Edition via Steam.
Use your favourite mod manager or skse64_loader instead. This may already be the practice for those who like SKSE-tied mods so the change might not even be that big in the end.