I recently reinstalled SOD on linux and ran through some issues, but here's what works for me now.
I'm on Fedora 37, AMD CPU and GPU, Gnome and Wayland for reference. I'm using the default Bottles installation. I used the instruction found elsewhere here to download the client via Steam and copied the files out to a separate Games folder. I have 2 installs for SOD as I run 2 different resolution monitors so I can have different client/UI setups.
1) Follow instructions provided on Wiki to get client from Steam or other source.
2) Follow wiki instructions to download and patch the sodpatcher.
3) Open Bottles and create a new game bottle and point it to your sod folder.
4) Change runner to sys-wine-8.0, and I think the rest I left default to dxvk 2.1, vkd3d-proton, and latency disable
5) In advanced Display Settings I enabled Virtual Desktop and set it to monitor size and enabled Fullscreen Mouse Capture, the rest of these options are off and renderer is GL pr Vulkan
6) Rest of the Settings I left at default
7) Go back to the Details page and scroll down to Legacy Wine Tools and click Configuration
8) Go to Libraries Tab, New Overrides, and pull down Dinput8.dll and Add it, and press apply/OK and close out this screen
9) I downloaded WinEQ2 and put the installer in a path the Bottle can see
10) In Details tab go to Legacy Wine Tools - Explorer, and use Explorer to navigate to WinEQ2 installer and install it, then run it and setup a SOD profile and desktop icon if you want one
11) Bottles should add a program link automatically for WinEQ2 after you run it. This is link I normally use to launch SOD. I find mouse control to be better using WinEQ, and a virtual desktop in wine. I can alt+tab to swap windows and mouse capture is perfect especially when rotating camera or strafing while turning left and right.
12) I created and other shortcut to sodpatcher and in the launch options deisable the virtual machine which doesn't seem to really disable it but if I don't it down't like launching the patcher otherwise. You can also just use Run Executable and choose sodpatcher directly if needed. You really only need to run it the first time and after patch days. The rest of time I use the WinEQ2 shortcut.
If you are only running 1 screen you probably don't need ALL of those steps as that's how I set mine up for 2 different clients running different resolutions on the same machine. The main tweaking is 1) setting the runner to wine8 and not soda 2) setting the override for dinput8.dll so you can see the proper zone names and some other bugs noted elsewhere, and 3) getting the clients to run as fullscreen windows for the good mouse capture.