I am a programming teacher for teenagers, and I am using LiveServer in Visual Studio Code.
When searching for something like 'blame' (GIT) in the history of the files they modified, it doesn't show up for me. They logged in with their GitHub accounts. Is there anything to check who modified and what modifications were made?
Sure, you can check what modifications were made in the Timeline View or git commit history, but probably not who did what.
If you're talking about Local History entries in your Timeline View, then no, Local History doesn't have any concept of who made the history entry or made specific changes in a history event with multiple changes.
If you're talking about Git / Source Control entries in your Timeline View, then presuming that the Live Share participants were not making commits from their own machines using their own author info (name and email) when committing, and that they weren't committing using their own author info from a shared terminal part of the Live Share session, then there also wouldn't be anything to differentiate commits as being made by a specific Live Share participant- let alone specific parts of a commit, which git has no mechanism for attributing changes to users at that level of granularity.
Even the undo history is shared between all participants with no differentiation or concept of who wrote what. See Can undo changes made by others #1439.