Refactor: Simplify case directory structure

The distinction between `open/` and `done/` directories for cases has
been removed.
All cases for a user now reside directly under the user's directory
(e.g., `<data_path>/<slug>/<case_id>/`).

This simplifies path management and eliminates redundant directory
traversals.

Key changes include:
- Removed `open/` and `done/` subdirectories in path resolution.
- Introduced a `paths::case_dir` function as a single source of truth
  for case directory layout.
- Updated various modules (`recovery`, `auth`, `routes`, `transcribe`,
  `tests`) to use the new path structure.
- Adjusted templates to reflect the simplified case status
  representation.

server/src/paths.rs

@@ -0,0 +1,10 @@
+use std::path::{Path, PathBuf};
+
+/// Absolute on-disk location of a case directory.
+///
+/// Single source of truth for the layout `<data_path>/<slug>/<case_id>/`.
+/// Use everywhere instead of inlining `.join(slug).join(case_id)` so the
+/// layout can evolve in one place.
+pub fn case_dir(data_path: &Path, slug: &str, case_id: &str) -> PathBuf {
+    data_path.join(slug).join(case_id)
+}