I was hoping I can cleanup some redundant stuff and create more space
You couldn't reduce significantly the size of an upstream repo from a downstream location.
That upstream repo is likely a bare repo, and even deleting a branch wouldn't change much (a branch is just a pointer, and the reflog of that repo would still have the reference of the commits for that branch.
All the commands mentioned in "Reduce git repository size" are local commands.
So even without increasing the disk space, you would still need an admin to go on that server an clean that repo for you.