When I try to connect to a GOG-lobby per direct IP, the host gets the error that can be seen on the attached screenshot.

We have the same versions.

So the host updated the GOG version with the Larian Vault patch, and you did not enable the preview of patch 1.0.40 in Steam?
That should be compatible, then.

Have you tried hosting and having the GOG player connect to you?

That is correct, we are all on 1.0.33.0. I will test the connection vice versa.

Alright, we verified that the ports are open and connections are working using netcat on port 23232 UDP. All versions are 1.0.33.0:

Host / Client <=> Host / Client
[GOG with VaultPatch] <=> [GOG with VaultPatch] = Working with warning that the client has a different version.

Host <=> Client
[Steam-Version 1.0.33.0] <=> [GOG with VaultPatch] = Not working, no error message

Host <=> Client
[GOG with VaultPatch] <=> [Steam-Version 1.0.33.0] = Working with warning that the client has a different version. Yesterday it did not work. The difference today is that I was joining a lobby with one player in the lobby, not two. Both had the same GOG-version.

Thanks for the additional testing. Maybe there is a difference between how the Larian Vault release stores the version information and GOG, that is causing the error?

The host always got the mismatching versions warning and we could play a longer match just fine with GOG on GOG. First time we tried I was kicked from the lobby after the version warning with steam as client and GOG as host, but we had another player in the lobby at that time with GOG patched with VaultPatch to 1.0.33.0 just like the host.

With my previous post it was the same host, this time only the host I was connected to with the steam-version as client. We did not start a game, though.

tl dr: It sounds unlikely to me and it is a question I recommend asking the developers.

OT: Were you able to get an answer to my question if it is possible to change nicknames and avatars in the gog-version's multiplayer (I Asked in a different thread)? The "invite friend"-button that works in the steam-version is without function in the gog-version, by the way. Just nothing happens when clicking it.

I'm certainly going to report the issue, it just seems strange there would also be a warning when the host and client are both playing the GOG version with the Larian Vault patch. Even if that were the cause of the problem, though, it shouldn't really be an issue.

No, I didn't get a response about changing multiplayer names or avatars. It seems like an obvious option to have, though (especially the names), so assume it would be on the to-do list.