Ok, problem found, but not explainable:

My friends and I tested several scenarios on my desktop computer: DX11/Vulcan Client starting from GOG Galaxy client and with the Exe, wired / wireless connection to the router, disabeling firewall, hotspot from phone,....

Except the hotspot everything showed the same result: do not work most of the time but once in while it suddenly is running until host is starting a new lobby.
A last thing I was testing, just to be sure that there are no problems with my computer: I grabbed a laptop from work, copied the game files on an external SSD, starting the game directly with the exe and... it worked! I was able to join several times also when a new lobby was created.

First thought: f@!§!!§k smile
I use my computer also with several virtual machines using Hyper-V. So maybe virtual switches could cause the problem... So my FRIENDS decided that I have to do a clean Windows installation. smile
So I installed Windows 11 from scratch just running OS, drivers and graphic card driver package. Then I started BG3 with the exe directly from the folder and it worked like a charme, tested with one of my friends. We decided to play in the evening a little bit and I continued installing several other things.

In the evenings same behavior as before: Cannot connect to the game! Hypervisor wasn't installed at that time... but GOG. I uninstalled GOG Galaxy, running the game as EXE and it worked. Without any problems.
And then the funny thing happened: The same problems started on one of my other friends. He then just killed every GOG related process, starting the game directly with the exe and everything worked fine.

Result:
GOG Galaxy caused the problem as long as it is running in the background. When it was running, I was not able to join the lobby in any way. I can see it, but I cannot join. Why? No idea...