The benefit of the WSL (and SSH and Docker) integration is that you still run the native version of VS Code for your OS, and just the server portion of VS Code runs on the 'remote' server. Running the whole of VS Code (or Codium or whatever) in WSL probably works but there'll be little annoying things with it since it's not running natively, for example you can't drag files from Explorer into it, can't have a PowerShell terminal open alongside a WSL one, etc.

I don't think the SSH integration is locked down, so I wonder if you could install OpenSSHd in WSL and connect vis SSH.