Refactor analyze recovery and worker busy status

The analyze recovery scan has been refactored to iterate through user
directories and enqueue pending analysis jobs more efficiently. The
`WorkerBusy` status has been introduced as an `Arc<AtomicBool>` to track
whether the analyze worker is currently processing a job.

This `WorkerBusy` flag is used in the `analyze::worker::run` function
and managed by a `BusyGuard` RAII struct, ensuring the flag is correctly
set and unset even in case of panics.

The `handle_my_cases` and `handle_case_detail` handlers in `user_web.rs`
now utilize the `WorkerBusy` flag to accurately display the "analyzing"
status and to trigger a self-heal of orphaned analysis inputs when the
worker is idle.

Additionally, the `WorkerBusy` type is now exported from
`server/src/lib.rs` to be accessible by other modules. The test cases
have been updated to include the `WorkerBusy` parameter when spawning
the analyze worker.

server/src/main.rs

@@ -81,10 +81,13 @@ async fn main() {
 
     // Analyze pipeline: channel + worker + recovery scan.
     let (analyze_tx, analyze_rx) = analyze::channel();
+    let worker_busy: doctate_server::WorkerBusy =
+        std::sync::Arc::new(std::sync::atomic::AtomicBool::new(false));
     tokio::spawn(analyze::worker::run(
         analyze_rx,
         config.clone(),
         http_client.clone(),
+        worker_busy.clone(),
     ));
     {
         let tx = analyze_tx.clone();
@@ -99,6 +102,7 @@ async fn main() {
         transcribe_tx,
         analyze_tx,
         session_store: doctate_server::web_session::new_store(),
+        worker_busy,
     };
 
     let addr = format!("0.0.0.0:{}", config.server_port);