I had previously brought Skyrim and had installed it through Steam with SKSE.
I recently brought Skyrim Anniversary Edition and wanted to use SKSE with it (Special Edition showing in Steam), but when I try to launch it, it looks up for Skyrim, the first installed.
How can I make it lookup for the new installation?
There are different versions of SKSE for each released version of Skyrim. If you previously bought the Legendary Edition of Skyrim (i.e. 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. You need to download the SE or AE version which is appropriate for your version of Skyrim.
It should be emphasized that "AE," in a modding context, usually refers to all 1.6.x and later versions of Skyrim, regardless of whether you actually bought the Anniversary Edition bundle (and "SE" usually means 1.5.97). If you're not sure which version you have, you probably have AE by default.
If you want to use the SE version of Skyrim (typically because you're using some SKSE mod that is not compatible with AE), you can use this tool to downgrade Skyrim to 1.5.97. 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). 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.
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. Some of these mods have not been updated for AE at all, and others are still in development. See this Reddit thread for further discussion of related issues.
