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/transient_failure_retries_test.rs

@@ -136,10 +136,8 @@ async fn transient_whisper_failure_is_reenqueued_and_recovers() {
         ".m4a.failed must not exist after transient error"
     );
     assert!(
-        !case_dir
-            .join("2026-04-15T20-30-00Z.transcript.txt")
-            .exists(),
-        "no transcript yet — the 503 produced nothing"
+        !case_dir.join("2026-04-15T20-30-00Z.json").exists(),
+        "no metadata sidecar yet — the 503 produced nothing"
     );
 
     // Act 2: heal re-enqueues the pending .m4a (second mock → 200).
@@ -154,22 +152,26 @@ async fn transient_whisper_failure_is_reenqueued_and_recovers() {
         )
         .await;
 
-    // Assert: the transcript lands. Poll because the worker runs
-    // asynchronously after the heal hands off the job.
-    let transcript = case_dir.join("2026-04-15T20-30-00Z.transcript.txt");
+    // Assert: the recording metadata sidecar lands. Poll because the
+    // worker runs asynchronously after the heal hands off the job.
+    let meta_path = case_dir.join("2026-04-15T20-30-00Z.json");
     let start = std::time::Instant::now();
-    while !transcript.exists() {
+    while !meta_path.exists() {
         if start.elapsed() > Duration::from_secs(10) {
             panic!(
-                "transcript did not appear within 10s (whisper hits: {})",
+                "meta sidecar did not appear within 10s (whisper hits: {})",
                 whisper.received_requests().await.unwrap().len()
             );
         }
         tokio::time::sleep(Duration::from_millis(25)).await;
     }
 
-    let body = std::fs::read_to_string(&transcript).unwrap();
-    assert_eq!(body, "recovered text");
+    let bytes = std::fs::read(&meta_path).unwrap();
+    let meta: doctate_common::RecordingMeta = serde_json::from_slice(&bytes).unwrap();
+    match meta.transcript {
+        doctate_common::Transcript::Content { text } => assert_eq!(text, "recovered text"),
+        other => panic!("expected Transcript::Content, got {other:?}"),
+    }
 
     // Teardown: close the worker channel so the background task exits.
     drop(tx_t);