Ah, darn :) I wanted to type Organizer but did Manager with all the naming confusion. Corrected that ;)

As for your versioning question:
GOG Skyrim SE is the latest game version 1.6.659.0.8 - the same as for Anniversary Edition, as the AE is only SSE + Creation Club DLC mods bundled currently. (ah! There, paladin181 was a bit quicker: same what he said)
There is no downgrade option below that as this is the first release iteration I guess. GOG is offering a downgrade functionality that will be usable from here on out, unless Bethesda is preventing it.
So if you currently want to run version 1.5.97 for Mod compatibility, you have to install the latest build from GOG, get the Downgrade Mod (e.g. from Nexus Mods) and downgrade with that to the older version.
You can also do that with AE but that may break the CC mods included in that (not sure).
As usual it is being worked on to upgrade and move along in time, so this is a current statement.

- There is a SKSE for the current version of AE that also is compatible and works with the current version of SE since they are the same build, but that might break some of the older mods that you wanted to apply.
- For better compatibility with older mods, the sweet-spot currently is somewhere at version 1.5.97. You can downgrade both game editions SSE and AE with the downgrade mod and get the older version of SKSE that is compatible with 1.5.97.

I would currently do the second option for greater choice of mods, not just the graphical ones but also mechanics and AI.
If you are going for visual mods only, you can stick to the first option.

I completely agree with this. It is a shame that Bethesda ended up splitting the modding and playing community that way.

To fil-cat and any who read my earlier post in this thread about the SE downgrade process/mod, I was wrong.

I believed the information to be accurate when written, but it was not, due to the following combination of reasons;

1. The mod has been updated (many times) since last visit to Nexus.
2. I did some (not enough) research into the Steam version system and decided I understood.
3. I decided I knew about how the mod works without even downloading it.
4. I have an existing, working Modded SE installation which I didn't want to disturb.
5. Worst of all, I failed to verify the facts behind my opinion before posting.

Having now tested the mod, it works. You can downgrade (on Steam) from 1.6.640 to 1.5.97.

Hubris + Vanity = Being wrong in public.

Good times, good times.

Does that downgrade mod actually work with the GOG version? I've hard that it does not. But can someone confirm whether it does or not?

EDIT: I made this post before I saw the post above this one that says the downgrade mod does work with GOG.

...which version number of SKSE would that be, exactly?

And from what link exactly does one acquire that version?

EDIT 3: I now realized that it seems I may have overlooked the part of the post above me this one that says "on Steam."

So does that mean that the downgrade mod does in fact not work on the GOG version after all, and therefore the GOG version is stuck being incompatible with many mods?

Thanks for checking and letting us know. I will change the information again ;)

You need to search the internet more, before asking ;)
SKSE can be easily found. In case you still havn't, the original page is https://skse.silverlock.org/
There you get detailed listings about what SKSE version to download for what Skyrim game version.

As for the Downgrades: it depends on which mod you are referring to.
LesTyebe was letting us know about an erroneous information given on the "Unofficial Skyrim Download" mod that also allows old game versions to be backported to via Steam - so that only works with the Steam repositories for a source.

As far as I understand the "Unofficial Skyrim Special Edition Downgrade patcher" is a standalone that includes the game version data. Running that it might automatically find your game install, if not you can point it to it.
You want to point it to the SkyrimSE.exe and NOT the SkyrimSELauncher.exe.
There are two versions for it on NexusMods: a "best of both worlds" that will only downgrade the game code but keep all the Anniversary Edition content and a "full patcher" that downgrades everything.

The file says "downgrade from 1.6.640.0 to 1.5.97.0", since that is the Steam versions numbering. GoG seems to be slightly higher up with its 1.6.659.0 (possibly because they have stuff like Creation Club and DRM excluded).
~It should still work I think.~ Nope, I checked both variants on Windows now: doesn't work with the GoG version yet. So currently that only works with the Steam versioning, no downgrading for GoG as of now. Give it some time. They probably will put up support for that too.

This will be solved by either a Downgrade Patcher update to also support the GoG version or the mod compatibility moving up over time. I'm not sure it is even possible to go beyond the release version on GoG to older versions prior to that because of the DRM-free nature, we simply don't have a DRM free version of 1.5.97.0 to apply.
So if you want to Downgrade and Mod the hell out of this right now -I mean RIGHT NOW, as of this very moment- you can only do that on the Steam version that has been around longer.
The GoG version is still very fresh. The coders are excited for a DRM-free version and getting at it ...

I can confirm that it starts and asks you to be pointed to your game since it can't find a Steam-Install.
I can't confirm on the GoG version yet, because I have that installed via Heroic games launcher on my Linux and I didn't manage to run Downgrade patch with Wine on there yet. I guess it would be the same problem as above under Windows.

Seems there is a text-limit to my initial post. I can't edit more text into it.

So here some additions for new-comers to modding...

Just to throw some more mentions out there for people new to modding:
"SkyUI" is a User Interface overhaul with lots of added functionality to the game and is essential for many other mods rely on, "SSE engine fixes", "Address Library for SKSE plugins" required for many mods, "Ultimate Immersion SE ENB" fixes lighting and adds meshes, "XPMSSE" for physics, "Nemesis" a behavior engine, "Immersive Citizens" fpr improved AI to NPC's ... and many more.

It can be confusing for starters. So why not rely on the prolonged experience of some who walked that path for many years? I'll mention "ESO" and "Ultimate Immersion" here (there are many others), go and look up their Youtube-Videos, Guides and ModLists.

If you are getting deeper down the rabbit hole you might want to manage and fine tune more yourself to your liking.
Again, just mentioning some tools here to help you get started:
"Vortex" from NexusMods is a ModManager, easy and convenient with all the Mods from there or ModLists for it.
More Powerful is "Mod Organizer 2", where you can micro-manage load orders and partial overwrites of mods.
"LOOT" is another tool taht helps you fix issues with your load order and dependencies.

Dnt get discouraged. Start easy.
This game can look awesome (depending on your hardware) and sooner or later you might crawl in there.

Have fun and happy gaming! o/

Reposted from here: https://www.gog.com/forum/general/release_the_elder_scrolls_v_skyrim_79ad7/post540

=)

About Mod Organizer 2:

I think we can confirm that MO2 (Mod Organizer 2) Team is working in making it support GOG's Skyrim SE/AE.
It seems it's really just a matter of MO2 recognizing paths, because it's plugins use precoded paths that aren't present in MO v2.4.4 for GOG's Skyrim, therefore it can't give the game directions to look for installed mods.
Right now they're trying to figure out a good way to make Skyrim plugin recognize if the game is Steam or GOG version and configure an instance accordingly.
Probably they will use GOG's Dlls present in 'GOGrim' installation and Steam's Dlls present in 'Steamrim' installation to give MO2 directions.

Sources:
https://github.com/ModOrganizer2/modorganizer/issues/1744
And their Discord.

About GOG's version compatibility:

Like GOG said in their announcement, users are being able to install many mods that do not require heavy scripted, or dll reading, because, as stated above, it's just a matter of path finding.
For heavy scriptied and dll dependant mods, it's up to mod authors to update their mod dlls to be compatible with GOG's SKSE (Skyrim Script Extender) version - I think.
So we can right now install many mods using Vortex mod manager, indeed.

Here are some that I'm personally going to test through Vortex:
These are not SKSE dependant, therefore they are 'easy to install' mods, with heavy compatibility.

Unofficial Skyrim Special Edition Patch
Carriage and Ferry Travel Overhaul
Better Dialogue Controls
Immersive Weapons
Immersive Armors
Immersive Patrols
Enhanced Blood Textures
No Spinning Death Animation
Point the way
Sounds of Skyrim Complete

--edit:

User LuckyTrixx posted this in MO2 issue linked above as a workahound for MO2 users:

Is anyone using vortex to Mod the COG The Elder Scrolls V: The anniversay addition. Vortex does not recognize the EXE files

i was but i switched to mod organizer 2 (MO2). seems daunting at first but really makes the install and loading of mods waaaay easier

I've downloaded the SKSE for the GOG version and can load the game through that in Vortex but none of the mods work even though they are all installed and enabled.

Did you follow the instruction and installed SKSE correctly?

Also, I highly recommend to use MO2.

my version of gog is running the mods from version 1.5.97 of skyrim and even oldrim mods from the 2011 version, I installed them all manually or using NMM and by the way they are running better than my steam via MO2

SKSE 2.2.6 and MO2 version 2.5+ works, but in some cases the problem is the mods need to be updated/modded to work with a different game version (for every update to a game some % of mods need an update).

The best solution would be a game modification that makes old mods backward-compatible with the new GOG release. I don't think that exists yet.