GOG uses a slightly different executable. GOG’s version 1.6.640 requires a (also on silverlock.org under "GOG SE build").
Installation is straightforward—manually dropping the .dll and .exe files into the Skyrim root directory remains the gold standard. Compatibility & "The Version Trap" skse 16640 link
Yes. Anniversary Edition is just the name for game version 1.6.640+ with Creation Club content. SKSE 2.2.3+ works perfectly with AE. GOG uses a slightly different executable
Title: Keeping Your Load Order Stable: The Complete Guide to SKSE 1.6.640 skse 16640 link