Refactor recording metadata to JSON sidecar

Replaces the `.transcript.txt` sidecar with a structured `.json` file
for recording metadata. This change consolidates transcript text,
duration, and other potential metadata into a single, extensible JSON
object.

This also refactors the `TranscriptState` enum to better represent the
on-disk state (absence of file means pending) and the in-memory
representation. The `Transcript` enum now specifically models the
terminal outcomes of the transcriber (`Silent` or `Content`).

The commit includes updates to documentation, data structures, path
handling, and various tests to align with the new metadata format.

server/tests/analyze_test.rs

@@ -1205,7 +1205,7 @@ async fn reset_case_clears_derived_and_unfails_audio() {
     assert!(dir.join("2026-04-15T09-05-00Z.m4a").exists());
     assert!(!dir.join("2026-04-15T09-05-00Z.m4a.failed").exists());
     // Derived artefacts gone.
-    assert!(!dir.join("2026-04-15T09-00-00Z.transcript.txt").exists());
+    assert!(!dir.join("2026-04-15T09-00-00Z.json").exists());
     assert!(!dir.join(ONELINER_FILENAME).exists());
     assert!(!dir.join(DOCUMENT_FILE).exists());
     assert!(!dir.join(ANALYSIS_INPUT_FILE).exists());
@@ -1235,7 +1235,7 @@ async fn reset_case_requires_admin() {
     assert_eq!(resp.status(), StatusCode::FORBIDDEN);
 
     // Nothing touched.
-    assert!(dir.join("2026-04-15T09-00-00Z.transcript.txt").exists());
+    assert!(dir.join("2026-04-15T09-00-00Z.json").exists());
     assert!(dir.join(DOCUMENT_FILE).exists());
 }
 
@@ -1282,8 +1282,8 @@ async fn bulk_reset_processes_multiple_cases_admin_only() {
     assert_eq!(resp.status(), StatusCode::SEE_OTHER);
     assert!(!dir_a.join(DOCUMENT_FILE).exists());
     assert!(!dir_b.join(DOCUMENT_FILE).exists());
-    assert!(!dir_a.join("2026-04-15T10-00-00Z.transcript.txt").exists());
-    assert!(!dir_b.join("2026-04-15T10-05-00Z.transcript.txt").exists());
+    assert!(!dir_a.join("2026-04-15T10-00-00Z.json").exists());
+    assert!(!dir_b.join("2026-04-15T10-05-00Z.json").exists());
 
     // Non-admin: bulk reset is rejected, dr_b's case untouched.
     let (cookie_doctor, csrf_doctor) = login_with_csrf(&app, &store, "dr_b", "s").await;
@@ -1299,7 +1299,7 @@ async fn bulk_reset_processes_multiple_cases_admin_only() {
         .unwrap();
     assert_eq!(resp.status(), StatusCode::FORBIDDEN);
     assert!(dir_c.join(DOCUMENT_FILE).exists());
-    assert!(dir_c.join("2026-04-15T11-00-00Z.transcript.txt").exists());
+    assert!(dir_c.join("2026-04-15T11-00-00Z.json").exists());
 }
 
 /// Regression guard: the bulk route handles *all* actions (including