Thanks so much for the solution, before I was playing with flatpack version, now I confirm that the game runs with vs_client_linux-x64_1.19.8 too.
Testet Single and Multiplayer
OS: Linux Mint 22 x86_64
Kernel: 6.8.0-49-generic
GPU: Intel CoffeeLake-S GT2 [UHD Graphics 630]
.net: dotnet-sdk-7.0
VS version: vs_client_linux-x64_1.19.8
Start Game: With the "Vintagestory" executable