safekeeper: include application name in wal service root span (#8525)

For IDENTIFY_SYSTEM in particular, application name gives away whether
the client is
* walproposer => Some(wal_proposer_recovery)
* safekeeper => Some(safekeeper)
* pageserver => Some(pageserver)

Context:
https://neondb.slack.com/archives/C06SJG60FRB/p1721987794673429?thread_ts=1721981056.451599&cid=C06SJG60FRB

safekeeper/src/handler.rs

@@ -143,7 +143,12 @@ impl<IO: AsyncRead + AsyncWrite + Unpin + Send> postgres_backend::Handler<IO>
                 self.tenant_id.unwrap_or(TenantId::from([0u8; 16])),
                 self.timeline_id.unwrap_or(TimelineId::from([0u8; 16])),
             );
-            tracing::Span::current().record("ttid", tracing::field::display(ttid));
+            tracing::Span::current()
+                .record("ttid", tracing::field::display(ttid))
+                .record(
+                    "application_name",
+                    tracing::field::debug(self.appname.clone()),
+                );
 
             Ok(())
         } else {

safekeeper/src/wal_service.rs

@@ -43,7 +43,7 @@ pub async fn task_main(
                     error!("connection handler exited: {}", err);
                 }
             }
-            .instrument(info_span!("", cid = %conn_id, ttid = field::Empty)),
+            .instrument(info_span!("", cid = %conn_id, ttid = field::Empty, application_name = field::Empty)),
         );
     }
 }