Im having similar problems.
I cant sign into Steam, it always fails and gives an error.
I can sign into GOG but have to do it every time I load the game if I want to do anything with cloud saves.
I cant switch between standard and GOTY versions without signing in again.

I can only see my switch save. I have a PS4 and PS5 versions saved there too but cant see those on the switch.
The PS5 version can see and use the PS4 save from GOG.
The PS4 can save to GOG. The PS5 can save to GOG. The Switch can save to GOG.
The PS4 acan see the PS5 and PS4 save.
The PS5 can see the PS4 and PS5 save.
The Switch can only see the Switch save.
PS4/5 cant see the Switch save.

So I've read for the last hour how all platforms have cross save working but they dont.

Now for a headache....
The Steam Deck (SteamOS) running the GOG version of W3 CANT sign into GOG so it cant get access to any cloud save.
on the Steam Deck running Windows 10 instantly sees the Switch version and runs it. Didnt even hsve to sign into coud or anything, it was just there.

Problem is the Switch version is about 2 hours gameplay/
The PS4 is about 20 hours gameplay.

Update for my problem and experience...
I did a new save on the PS5 and send that to GOG.

The Switch can now see it about 6 hours later.

BUT it says the save is from a newer version so it cant be loaded.

So we have to wait for the Switch version to get v4.0 update as thats what the PS4/5 are running. The Switch is still on v3.7

maybe when the switch version gets the v4 update these problems will be fixed.
But with everything Switch it'll take months before its released.
Hopefully it'll be days for this not months like every other Switch game.

I understand your frustration with the lack of response and support regarding the issue you're experiencing with the GOG interface on the Switch version of The Witcher 3. It can be disappointing when your concerns are not addressed promptly or effectively. It's unfortunate that the support ticket on GOG.com did not yield the desired results.

Raising the issue with the dedicated support team at support.cdprojektred.com/en/witcher-3/nintendo-switch is a good step to take. By submitting your ticket there, you are reaching out to the appropriate channel specifically for the Switch version of the game. Hopefully, they will respond and provide assistance in resolving the problem you're facing.

While waiting for a response, it might be helpful to explore alternative resources such as online forums or communities where other players might have encountered similar issues and found solutions. Additionally, consider sharing your experience and feedback with other Switch users who are also affected by the problem. This way, you can collectively highlight the importance of addressing the issue and encourage the developers to take action.