Git’s model is fundamentally different than TFVC. You need to commit the file to your branch (you don’t necessarily need to push the change or the branch to the remote server). Once you commit the change, switching branches will behave in the fashion you’re expecting.
Git is based on the model of committing changes to local branches frequently. Even if the code doesn’t yet compile, it’s fine to commit it to a local branch… you can always rebase or cherry-pick later on.