In case this is useful to anyone, after hours trying to change things from the Docker Desktop GUI or settings.json or deamon.json, etc to avoid storing the app and the data in C:, I finally found the only way that fully worked to me is to simply:

1. uninstall Docker Desktop
2. reinstall it with a command line like this (for example here in my F:\Docker folder):

"Docker Desktop Installer.exe" install --accept-license --installation-dir=F:\Docker\bin--wsl-default-data-root=F:\Docker\wsldata --hyper-v-default-data-root=F:\Docker\hvdata

If will work if you choose WSL2 or Hyper-V as the backend (if you switch to Windows container instead of Linux containers this will be needed).

PS: make sure the target folder, (such as F:\Docker in my case) has needed rights (whatever that means for Docker or its services) otherwise you'll get other cryptic errors like "Unexpected WSL error", etc.