nix <cmd> --update-input ... fails in detached git worktrees

Describe the bug

nix <cmd> --update-input ... fails when the following conditions come together:

1. when called in a git worktree, i.e. when .git is a file (pointing to the real repository) instead of a directory.
2. when the worktree is clean

It reports the worktree as a shallow clone and that it needs a deep clone to update the inputs.

error: '/path/to/repo' is a shallow Git repository, but a non-shallow repository is needed

       … while fetching the input 'git+file:///path/to/repo'

Steps To Reproduce

1. Enter a git repo with a flake that has inputs.
2. Create a worktree with git worktree add ../workree branch
3. cd ../worktree
4. nix flake lock --update-input <input> or any other command that accepts the --update-input option

Expected behavior

Updates the input.

nix-env --version output

2.4

Workaround

1. Run nix <cmd> --update-input <input> path:., which forces nix to interpret the flake URL as a path and avoids the git+file:// codepath.
2. Modify any tracked file (not necessarily flake.lock) to make the tree dirty, also solves the issue.