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/tests/web_test.rs

@@ -63,7 +63,7 @@ async fn web_index_shows_cases() {
     let case1 = "550e8400-e29b-41d4-a716-446655440000";
     let case2 = "660e8400-e29b-41d4-a716-446655440000";
 
-    let open_case = data_path.join("dr_test/open").join(case1);
+    let open_case = data_path.join("dr_test").join(case1);
     std::fs::create_dir_all(&open_case).unwrap();
     std::fs::write(
         open_case.join("2026-04-13T10-30-00Z.m4a"),
@@ -71,7 +71,7 @@ async fn web_index_shows_cases() {
     )
     .unwrap();
 
-    let done_case = data_path.join("dr_test/done").join(case2);
+    let done_case = data_path.join("dr_test").join(case2);
     std::fs::create_dir_all(&done_case).unwrap();
     std::fs::write(
         done_case.join("2026-04-12T09-00-00Z.m4a"),
@@ -125,7 +125,7 @@ async fn web_audio_serves_file() {
     let data_path = config.data_path.clone();
 
     let case_id = "770e8400-e29b-41d4-a716-446655440000";
-    let case_dir = data_path.join("dr_test/open").join(case_id);
+    let case_dir = data_path.join("dr_test").join(case_id);
     std::fs::create_dir_all(&case_dir).unwrap();
 
     let audio_bytes = b"fake audio content for test";