Unless you open the game with the SKSE launcher, SKSE wont be working, and mods that.
Some of these mods have not been updated for AE at all, and others are still in development. To have SKSE working while you play, you need to use the SKSE launcher. If you intend to install any SKSE-based mods which contain native code (.dll files), you will need to ensure that you download the version of those mods appropriate to either SE or AE. The differences between 1.5.97 and 1.6.x are very minor and generally do not affect gameplay or stability to any noticeable degree. You will still be able to use all of the new content in Anniversary Edition (provided you choose the "best of both worlds" version of the downgrader), but it will be compatible with the SE version of SKSE (because AE is ultimately "just" an updated SE with some extra DLC, rather than an entirely separate game as Legendary Edition was). Confirm you have original Skyrim installed.
The current recommendation is to use this tool to downgrade Skyrim to 1.5.97. Many mods work now with Address Library plugin which means if you update your Skyrim from Steam and install the corresponding SKSE version all mods using. If neither was your problem, then either SKSE or SkyUI was not installed. When trying to launch SKSE Steam just terminates the application You can read more. Note also that the AE version of SKSE is still marked "preliminary," meaning that it is still under development and might not work exactly right. You need to download the SE or AE version which is appropriate for your version of Skyrim. the version before there was a "Special Edition"), then the SKSE for that version of Skyrim is incompatible with Special/Anniversary Editions of the game. If you previously bought the Legendary Edition of Skyrim (i.e. There are different versions of SKSE for each released version of Skyrim.