The Skyrim version I recently downloaded said it is the Special Edition, but it is installed in a Skyrim Anniversary Edition folder.
I am a little confused, is this a GOG mistake, or a real problem?
Will this be a future problem?

All is as it should be.
Both GOG versions are exactly the same.
The only difference is the extra CC content that is installed separately as a DLC with the Anniversary Edition.

When Skyrim was first released, it was a 32bit application. This original version is usally referred to as Legendary Editon (LE).
2011 Bethesda re-released Skyrim as Special Editon (SE), now a 64bit application which included all 3 official DLC that were individually perchaseable for LE. Content-wise, both versions are identical, there is nothing added or canceled (that includes all the bugs that were sitll present in LE). Over time, Bethesda released a few patches for SE to address some issues. But after launching the Creation Club feature, patches are now a coming in quite often to keep the base game compatible with all the new CC content.
In November 2021, at game version 1.59xx, Bethesda released the Anniversary Editon. This is NOT a re-release of the game, unless you consider recompiling of the executable with a newer version of the compiler a re-release. Technically it is just an other update to SE (patch levels 1.6xxx+). Every owner of Skyrim SE gets this if they do not actively prevent the game from updating. This "free" update also includes 4 items from the CC list. The rest of the CC mods (over 70 more) are not free for everyone. If you want them, you must buy the Anniversary upgrade, which is not required to play the game of course.
TL,DR: Anniversary Edtion = Special Editon with version numbers 1.6+. Don't get confused by the names.