Neither the .git folder nor a project folder where the .git folder resides is a repository. The fact that it is completely fine to add several remote repositories to the same .git folder proves (from the formal logic perspective) that a repository is something different from a folder.

Long story short, there is no consistent definition of what a Git repository is. Each definition highlights the essence of the "phenomenon" from a perspective that matches a certain theoretical context in an educational materials and technical documentation.

In practical usage where Git is referenced I heard the following definitions "git/repository is a folder", "git is a control version system", "git/repository is a list of changes in the project files", "git/repository is an account", "git/repository is a storage".

I know that when you git commit, you are logging changes into your local .git folder.

This was very confusing to me (and I suspect not only for me) when I was learning Git, so let me comment on it.

When we make a change in a project file or a folder Git tracks these changes unless we explicitly tell Git to not track the changes with .gitignore. However, only the information of some certain changes we want to save, that's why we manually select what to commit. When we use git add * we're also making a selection - in this case, literally selecting "everything".

Since any information needs to be stored somewhere, regardless of its type, the commits we make must also be stored somewhere. We have to assign a name to this place to reference it later. The harsh truth is that, for the human mind it's not really that important whether we call this place a repository, or a hash table, or database,a Git folder or anything else.

From my personal perspective, when I git commit, I log the commit to the .git folder not because I do it deliberately or intentionally, but because I am committing to a place I call "a repository". This repository has a relationship with the .git folder, and this is the relation of relative location - the repository is situated within the .git folder. By logging the information about the change to the "repository", I inevitably modify something inside the .git folder.