Whether the server has a working tree does not affect clients that directly clone the remote repository.
In any case, they will receive a full copy of the remote repository objects, and in the initial clone, a local branch will be configured to track the default branch of the remote repository (usually this is a wizard), and this local branch will be checked.
It is usually recommended that the remote repository be exposed, since an attempt to click on a marked branch will cause the remote working tree to no longer synchronize with the selected branch. Usually for a remote repository there is usually no working tree.
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