If you can SSH into your university system from your WSL, I assume you can directly SSH from you Windows system. In that case, you can setup VS Code Remote SSH from Windows to directly access your university systems. Given that, I used a Git Bash terminal, as it supports all Linux commands right from your Windows OS.
Step 1: Setup your SSH access (password-less or not) to your university's systems. You can refer articles online, I assume you already know how to do that since you did it from within WSL.
Step2: Install the remote development package in VS Code extensions in local machine.
Step 3: Go to VS Code Settings and expand the Extensions drop down and select 'Remote - SSH'. On the settings page, set the "Remote - SSH: Config File" to the an ssh config file where you will store remote system details. E.g.: ~\vscode.ssh
Also select the checkbox for ‘Always Reveal the SSH terminal’.
Step 4: Add the remote system details to the file ~\vscode.ssh like:
Host <hostname>
User <ID for SSH login> # e.g. your university ID
HostName <full qualified address for your remote system> # e.g. system.subnet.university.edu
IdentityFile <your SSH pvt key> #e.g. ~/.ssh/id_rsa
Step 5: Select Remote Explorer on left navigation bar and "SSH Targets" from the dropdown. Your hostname should appear here. Right click and connect to Host.
Step 6: Carefully watch the logs of your first connection attempt from VSCode terminal logs if there are any failures to extract tar files.
By default, VS Code installs the vscode-server in your remote system's home directory, which may run out of space based on your university's space restrictions. You need to move your vscode-server directory to a work area where there's less space restrictions, usually a project area. Use below steps to do this, I created these for my organisation's use:
Once you start VSCode remote, the connection may fail or succeed based on the free space in your remote home directory as by default, VSCode setups your remote server in home directory, and this cannot be changed.
If success, still move vscode-server to another large free space directory:
a. Navigate to a desired project space directory from remote desktop terminal
b. mv ~/.vscode-server /your/big/disk/project/space
c. ln -s /your/big/disk/project/space/.vscode-server ~/.vscode-server
d. Use full absolute paths in previous command to avoid cyclic links. Confirm with below command, it shoud not return anything.
$ find -L ./ -mindepth 15
e. Reconnect from your VSCode again
If failed, manually setup vscode-server on remote large free space directory:
a. Get vscode-server commit ID on remote server using below command, which would be like 'e2d4cc38bb5da82wb67q86fd50f84h67bb340987'
$ ls ~/.vscode-server/bin
b. Download tarball replacing $COMMIT_ID with the the commit number from the previous step on local system: https://update.code.visualstudio.com/commit:$COMMIT_ID/server-linux-x64/stable
c. Move tarball to remote server disk from local system:
$ scp -P 22 vscode-server-linux-x64.tar.gz remoteID.remote.system.url.com:~/
d. Move tarball to large free space directory as below:
$ mkdir -p /your/big/disk/project/space/.vscode-server/bin/$COMMIT_ID/
$ mv ~/vscode-server-linux-x64.tar.gz /your/big/disk/project/space/.vscode-server/bin/$COMMIT_ID/
e. Extract tarball in this directory
$ cd /your/big/disk/project/space/.vscode-server/bin/$COMMIT_ID
$ tar -xvzf vscode-server-linux-x64.tar.gz --strip-components 1
f. Create symlink of .vscode-server in your home directory
$ ln -s /your/big/disk/project/space/.vscode-server ~/.vscode-server
g. Connect again