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/routes/case_actions.rs

@@ -45,13 +45,14 @@ pub async fn handle_close_case(
         ));
     }
 
-    // Close only acts on cases in open/. A case in done/ is already finalized.
     let user_root = config.data_path.join(&user.slug);
-    let case_dir = user_root.join("open").join(&case_id);
-    if !tokio::fs::try_exists(&case_dir).await.unwrap_or(false) {
-        warn!(slug = %user.slug, case_id = %case_id, "close: case not found in open/");
-        return Err(AppError::NotFound("Case not found".into()));
-    }
+    let case_dir = match locate_case(&user_root, &case_id).await {
+        Some(p) => p,
+        None => {
+            warn!(slug = %user.slug, case_id = %case_id, "close: case not found");
+            return Err(AppError::NotFound("Case not found".into()));
+        }
+    };
 
     let input_path = case_dir.join("analysis_input_v1.json");
     if tokio::fs::try_exists(&input_path).await.unwrap_or(false) {
@@ -113,11 +114,13 @@ pub async fn handle_reanalyze_case(
     }
 
     let user_root = config.data_path.join(&user.slug);
-    let case_dir = user_root.join("open").join(&case_id);
-    if !tokio::fs::try_exists(&case_dir).await.unwrap_or(false) {
-        warn!(slug = %user.slug, case_id = %case_id, "reanalyze: case not found in open/");
-        return Err(AppError::NotFound("Case not found".into()));
-    }
+    let case_dir = match locate_case(&user_root, &case_id).await {
+        Some(p) => p,
+        None => {
+            warn!(slug = %user.slug, case_id = %case_id, "reanalyze: case not found");
+            return Err(AppError::NotFound("Case not found".into()));
+        }
+    };
 
     let current_version = find_latest_document(&case_dir)
         .await
@@ -166,8 +169,8 @@ pub async fn handle_document_view(
         .map_err(|_| AppError::BadRequest("Invalid case_id".into()))?;
 
     let user_root = config.data_path.join(&user.slug);
-    let (case_dir, _status) = match locate_case(&user_root, &case_id).await {
-        Some(v) => v,
+    let case_dir = match locate_case(&user_root, &case_id).await {
+        Some(p) => p,
         None => {
             warn!(slug = %user.slug, case_id = %case_id, "document view: case not found");
             return Err(AppError::NotFound("Case not found".into()));