I got it to work!

Situation: I purchased Skyrim Anniversary Edition from GoG.
Installed to C:\Games\Skyrim - I'll refer to this directory as [Skyrim]
I downloaded the Creation Kit from Steam.
Steam client is installed in C:\Games\Steam - I'll refer to this directory as [Steam]

Click on "Launch" in the Steam client, the button changes to "Stop", there seems to be a popup in the lower right corner, but before you can actually blink an eye, the button says "Launch" again - and that's it.

In the Steam client, click on the cogwheel (Tooltip: "Manage"), go to "Manage" (I know. Stupid innit?) and select "Browse local files" from the 2nd level menu (which should have been the 1st). This will open [Steam]\steamapps\common\Skyrim Special Edition\

If you run CreationKit.exe there, you at least get a decent error message:
The code execution cannot proceed because steam_api64.dll
was not found. Reinstalling the program may fix this problem.

Now here's the crucial question: Do you have an nVidia graphics card?
If so, open C:\Program Files\NVIDIA Corporation\NvStreamSrv\ and: Lo and behold! - steam_api64.dll.
(Well: I simply did a search for it on my C:\ drive. Chances are, other graphics card vendors also include some entirely superfluous stuff which require a dummy steam dll, so give it a try!)

Important: Please do *NOT* download "steam_api64.dll" from any website claiming to host every dll under the sun!
How, do you think, they do not get into troubles for copyright issues? At best, the dll is completely bogus (in which case, any program which relies on them might start - but crashes when it actually makes any function call) and at worst...well, a dll is actually a kind of program, running on your computer with your permissions...I could think of a few things you really would not appreciate.
Of course, I do not stick to my own advice! What do you think I am? clever? Nooo...
So if you do this (in a VM!) your efforts will be rewarded with a different error message like "Could not find entry point steamapps in steam_api64.dll - that's how you know it is completely useless as propably every program loading steam_api64.dll will make a function call to "staemapps".

But the steam_api64.dll from C:\Program Files\NVIDIA Corporation\NvStreamSrv\ actually did the trick!
Copy it to the Steam creation kit folder ([Steam]\steamapps\common\Skyrim Special Edition\ - and nowhere else!) and run CreationKit.exe. Look ma! it's working! it wants to unzip "Scripts.zip"!

If you do not actually want to create mods, click "No". Otherwise, let it do its thing. I wasn't surprised to see the warnings for the missing *.nifs at first. The whole lot was still in [Steam]\steamapps\common\Skyrim Special Edition\ which was otherwise completely empty. So I copied the whole shebang into my [Skyrim]-folder. To clarify: copy the contents of the whole directory right into your game directory. "CreationKit.exe" is in the same folder as "SkyrimSE.exe".

Run CreationKit.exe...sad face. Same warnings. Click "Open file"...uh oh. No good. Nada. Damn.
The fact that the creation kit doesn't even find the plugins/masters is, as has been pointed out in this thread, a killer.

Head to Nexusmods and search for: "creation kit downgrade" in the Skyrim Special Edition section (because: "You cannot post any links at this moment" - grr!). Ignore the instructions, as usual.

Instead, scroll down to "CREATION KIT DOWNGRADE PATCHER":
"Downgrades the new Steam Creation Kit back to the way it was from Bethesda.Net so you can use the Creation Kit Fixes." - now that sounds useful, doesn't it?
Download the file "Patcher.exe-67096-1-6-438-0-1-5-73-0-1650919182.exe" (really?) and run it. It will fail to locate the Creation Kit, as expected. So point it to your [Skyrim] folder and select "CreationKit.exe". Click "Start Patching".
Now run the CreationKit.exe. You should see no warnings. If you click on the "Open file" icon, it will list your plugin/master files. I think you deserve a beer.

Stuff that might - or might not be - optional:
I don't know about you, but I actually intend on using the creation kit. So scroll a bit further on the nexus page to where it says "SSE Creation Kit Fixes", click the link and download "CK64Fixes Release 3.2-20061-3-2-1616560054.zip". Unzip right into your [Skyrim] folder. It opens a nice log window in the background the next time you open the creation kit, which seems to display some gobbledygook at first but actually could be quite handy in the long run.

Stuff that is certainly not optional:
Just one more thing: open CreationKit.ini in your [Skyrim] folder using any text editor. At the top, where it says:
[General]
bUseVersionControl=0
insert a new line:
bAllowMultipleMasterFiles=1
and save. This is necessary because your [Skyrim]\Data folder contains more than one *.esm-file which you might want to be able to load, since...well, that's another story.

Test case:
I use MO. I downloaded "A Quality Worl Map" (IcePenguinWorldMap.esp) - which gave me a warning in MO. Something like: this plugin uses Form 43 instead of 44. This means it's made with an older version of the creation kit. Simply open it in the latest creation kit and save it. Or something like that. So i copied "IcePenguinWorldMap.esp" from C:\Games\Mod Organizer\mods\A Quality World Map\ to [Skyrim]\Data and renamed the original to "IcePenguinWorldMap.bak" (you never know). Open the creation kit, load "IcePenguinWorldMap.esp" as active file (it was here that the log in the background reported some "interesting" things - but this being a rather "special" plugin, that was only to be expected) and save it. Moved it back to C:\Games\Mod Organizer\mods\A Quality World Map\ and run MO. No more warnings. Call me a nerd, but that kind of thing pleases me. Run the game, open the map. Yepp. It's there. And working. Yay!

HAPPY MODDING FOLKS!

PS: (authoritative voice) The "Construction Set" - as it was named back then - was always released after the game. Even for Morrowind. Trust me: I'm on terra firma here. There was a one CD version which just contained the game. If you got it, it's propably a good idea to get in touch with Sotheby's.
In case of Morrowind, it only took a few weeks for it to be released on 2 CDs, the 2nd one was the Construction Set and the original textures, unpacked as *.dds files, so you could actually make them look better. You wouldn't believe how much I loved "bsapacker". Anyhow. Have a good night!

So it was 2 CDs, one having a SEPERATE install for creation kit? Meaning it wasn't included in the installation of Morrowind?

Yes, I have the US Morrowind Collector's edition and it has a 2-CD flipper jewel case with the game and construction set on separate CDs.

That still not takes away that i's circumventing the Steam DRM. It does not matter if it's open source or not. If GOG would include that without explicit permission from both Steam and Bethesda, they would be in a world of legal trouble.

Sure - We as end user can use that stuff without getting sued, but it's a whole different story if you are a company that provides official installers. In short - GOG cannot provide that creation club stuff without permission. The only one that can do that is Bethesda. They have the source code of the game and Creation Club add-on, and they can "tweak" those executables to be no longer depending on Steam.

I do not say that Creation Club stuff cannot be made workable by us end users, but it cannot officially be provided by GOG, unless Bethesda provide GOG with the official corrected executables. Until then GOG is powerless to do anything, and it's unfair to blame GOG for anything in that matter. They certainly not going to take actions that risk getting in legal trouble with Bethsda and/or Steam.

Incorrect. FlanFlanSu is correct, as stated in their post.

I purchased the original Morrowind on CD long before I separately purchased the Tribunal and Bloodmoon on individual CDs.

Morrowind came with a game CD and a "Construction Set" CD.

I still have them, and the box they came in.

This works. I have done it myself (using Mod Organizer2)
https://www.gog.com/forum/elder_scrolls_series/skyrim_creation_kit/post32