While I do not have a ready-made solution for you as it depends a bit on what kind of setup your faculty uses, there are few options you could explore, if you haven't already.
The most straightforward one is to use the ".vscode/extensions.json" file as part of the project files themselves. When a new user starts working on the project (opens the cloned or extracted folder) then VS Code will recommend the necessary extensions. The latest versions get downloaded, installed to the user's AppData folder, and are ready to go.
There is also an approach for those not faint of heart. In it, you use a temporary user account to install the necessary extensions, and then copy the ".vscode" folder from that user's home directory either to "C:\Users\Default" (for non-domain joined computers) or to files associated with a Group Policy (for domain-joined computers).
For non-domain joined computers, any new users created on the computer get a set of extensions ready and baked. After opening VS Code they will likely get updated since new versions of extensions are released all the time. This approach does not work for user accounts that exist before the files are copied over.
For domain-joined computers note that the files in the Group Policy point to a very specific version of an extension and if ever a new version gets published VS Code may try to install that for the user. When the GP detects that the files have changed it may attempt to revert the changes back to the original set, unless the policy is configured correctly to allow updates from the users.
This latter approach may also break down horribly if a new version of VS Code gets released that maintains the extensions in a different manner or method. The ".vscode\extensions.json" as part of project files is much more robust.
