fix: change start date of lifecycle after running status

internal/session/lifecycle/lifecycle.go

@@ -46,7 +46,7 @@ func New(conn ssh.Conn, forwarder Forwarder, slugManager slug.Slug, port portUti
 		channel:         nil,
 		forwarder:       forwarder,
 		slug:            slugManager,
-		startedAt:       time.Now(),
+		startedAt:       time.Time{},
 		sessionRegistry: sessionRegistry,
 		portRegistry:    port,
 		user:            user,
@@ -97,6 +97,9 @@ func (l *lifecycle) SetStatus(status types.SessionStatus) {
 	l.mu.Lock()
 	defer l.mu.Unlock()
 	l.status = status
+	if status == types.SessionStatusRUNNING && l.startedAt.IsZero() {
+		l.startedAt = time.Now()
+	}
 }
 
 func (l *lifecycle) IsActive() bool {