Refactor transcript file handling to use JSON metadata

This commit changes the way transcriptions are stored and accessed.
Instead of using plain text files (`.transcript.txt`), transcriptions
will now be part of a JSON metadata file (`<stem>.json`). This allows
for richer metadata to be stored alongside the transcript, such as
duration, and provides a more robust mechanism for tracking
transcription states.

The changes include:
- Updating documentation and code to reflect the new `.json` file
  extension.
- Modifying file handling logic to read and write JSON metadata.
- Adjusting tests to accommodate the new file format.

server/src/analyze/auto_trigger.rs

@@ -319,10 +319,10 @@ mod tests {
     }
 
     /// Seed a `<stem>.json` next to a (presumed already-touched)
-    /// `<stem>.m4a`. Variant is `Transcript::Silent` because these
-    /// tests historically used an empty `.transcript.txt`, which
-    /// mapped to `TranscriptState::Silent`. Tests that need real
-    /// content call `seed_meta_with` with the desired variant.
+    /// `<stem>.m4a`. Variant is `Transcript::Silent` — these tests
+    /// only care that the recording is in *some* terminal state
+    /// (transcribed), not what was actually said. Tests that need
+    /// real content call `seed_meta_with` with the desired variant.
     async fn seed_meta(case_dir: &std::path::Path, stem: &str) {
         crate::paths::write_recording_meta_sync(
             case_dir,