The following steps worked for me:

Run the following command inside WSL to check if VS Code is installed:

code --version

If this gives an error, install VS Code Server inside WSL:

wget -qO- https://aka.ms/install-vscode-server/setup.sh | bash

If VS Code is installed but still not working, try reinstalling the remote:

rm -rf ~/.vscode-server
rm -rf ~/.vscode
code .