test(sync): await connection attempts instead of status notifications

Five sync tests waited for relay connections with
connect().and_wait(30 s). That call checks the relay status and then
subscribes to status notifications; a loopback connection that completes
between the two is never observed, and the caller sleeps for the whole
timeout. Under scheduler pressure this turns a sub-millisecond connect into
a 30 s stall.

Use the shared connect_client helper, which awaits the connection attempts
through try_connect and fails the test if any relay refuses.

Validation: the sync test binary passed (114 tests, 1 ignored) after the
change; formatting and all-targets Clippy with warnings denied pass.

Assisted-by: Claude Fable 5.1
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

tests/sync/historic_sync.rs

@@ -454,7 +454,7 @@ async fn test_pagination_for_large_historic_sync() {
         .add_relay(syncing.url())
         .await
         .expect("Failed to add syncing relay to client");
-    client.connect().and_wait(Duration::from_secs(30)).await;
+    crate::common::relay::connect_client(&client).await;
 
     // Poll until every issue has paginated across, up to a bounded deadline.
     let deadline = tokio::time::Instant::now() + Duration::from_secs(30);

tests/sync/live_sync.rs

@@ -486,7 +486,7 @@ async fn test_live_sync_layer3_events() {
             .authenticator(SignerAuthenticator::new(temp_keys))
             .build();
         if client.add_relay(relay_b.url()).await.is_ok() {
-            client.connect().and_wait(Duration::from_secs(30)).await;
+            crate::common::relay::connect_client(&client).await;
 
             let fetch_filter = Filter::new().kind(Kind::Comment).id(comment_id);
 
@@ -642,7 +642,7 @@ async fn test_live_sync_event_ordering() {
 
     let events_found: Vec<Event>;
     if client.add_relay(relay_b.url()).await.is_ok() {
-        client.connect().and_wait(Duration::from_secs(30)).await;
+        crate::common::relay::connect_client(&client).await;
 
         let filter = Filter::new().kind(Kind::GitIssue).author(keys.public_key());
 

tests/sync/purgatory_fetch.rs

@@ -159,10 +159,7 @@ async fn purgatory_fetch_batches_available_tips_and_isolates_missing_oids() {
         .add_relay(source.url())
         .await
         .expect("add source relay");
-    source_client
-        .connect()
-        .and_wait(Duration::from_secs(30))
-        .await;
+    crate::common::relay::connect_client(&source_client).await;
     source_client
         .send_event(&source_announcement)
         .await
@@ -239,10 +236,7 @@ async fn purgatory_fetch_batches_available_tips_and_isolates_missing_oids() {
         .add_relay(mock.url())
         .await
         .expect("add mock relay");
-    mock_client
-        .connect()
-        .and_wait(Duration::from_secs(30))
-        .await;
+    crate::common::relay::connect_client(&mock_client).await;
     mock_client
         .send_event(&syncing_announcement)
         .await