What exactly means "broken"? And are you saying that the recent Morrowind update for Galaxy caused it?
OpenMW has its own savegame management, and its savegames have always been incompatible with Morrowind's. I'd be surprised if OpenMW cared for Galaxy cloud saving in the least.

Apologies if this is too obvious to mention, but OpenMW is not Morrowind or a mod. It is a different game on a different engine. Inconsistencies with Galaxy can likely be worked around, but are understandable.

That is exactly what I am saying. It worked before the update, and now it does not (at least: Galaxy was "reporting" it as working).

Yes, I am aware of this: one is somewhat a huge reverse engineer of the other, but is now essentially an engine in its own right.

That would be a shame, but understandable.
It's OK: you have good manners.

It has become an engine of its own, but started as a "reverse engineer" of the codebase that runs Morrowind, that's why OpenMW can make use of the Morrowind code to run it, but other games could be run on it too.

I agree. I've tried something out, but it doesn't seem to be working.

OK. But what exactly doesn't work? What do you do, and what do you observe? "Broken" tells me that you think or notice that something doesn't work, but not what it is. Without more information it 's imossible to assess the situation for an outsider. If you're interested in assessments / comments / attempts to help from outsiders at all.

If you didn't try it already, you could perhaps find help on Steam. How to get OpenMW running on Steam (which I suppose isn't so very different from Galaxy) has been discussed there, too.

Thanks for sharing you may actually be interested in an informal diagnostic:

As I stated previously, the Cloud Saves function has stopped, since this update took place.

I've tried copying my OpenMW saves to the vanilla Saves folder, to see if that prompts a change, but it didn't work.

It also appears to only be Morrowind that's affected; I'm assuming this means I will need to reinstall Galaxy.

I was thinking about logging a tech' support ticket with GOG, but I thought I'd ask the community for ideas first.

Thanks. But I still don't know what worked before and doesn't work now: Cloud saving in Galaxy for Morrowind, or for OpenMW? I don't use Galaxy, and I don't use cloud saving at all, but it is my understanding that cloud saving in Galaxy "should" work for Morrowind, but not necessarily for OpenMW. "Not necessarily" means that it could possibly be enabled by using some tricks (it's why I mentioned Steam).

If it doesn't work for Morrowind since the latest update, then something must have gone wrong, caused by the update or by something else which happened at about the same time. And I suppose other players would be affected, not just you. With other words: If it's just you, it's likely that it wasn't caused by the update (at least not by the update alone).
I can't say what the best way forward could be for you. To ask the community was a good idea. You may ask again, with a clearer problem description. To report the problem to GOG might help, too - if other users reported the same problem to them. If it's just your problem, and they can't reproduce it, there is not much they can (and probably want to) do.
Is there a "repair" process for Galaxy (like Steam's verification), or at least for Morrowind? One of the most common reasons for problems is missing or corrupted files. If yes, I'd try it. Full un- and re-installation of Galaxy and/or Morrowind could be a last resort (would probably mean a lot of work, a risk to create new problems, and no guarantee that the original problem will have gone).

On the other hand, if you had a working cloud saving process for OpenMW before the recent Morrowind update, and it doesn't work anymore, then I'm afraid you'll have to find a solution yourself - I wouldn't expect GOG (or anyone else) to make sure that Morrowind updates are compatible with OpenMW cloud saving (which isn't even native for OpenMW). You must know how you enabled cloud saving for OpenMW, and could try to fix it. If other Galaxy users do the same, they might be able to help you.

I'd also consider using another cloud-saving process for OpenMW (using, for example, OneDrve).

Understood: thanks for the assistance.

I suspected Cloud Saves were only working by "sheer dumb luck", but for clarification they did work for Morrowind and somehow for OpenMW before this update.

It seems to be neither of them, now.

The only proper feedback I have is what Galaxy tells me, it could be that the error message is at fault, I don't know.

Anyway: thanks.