A handler's panic is logged and counted as 500 (closes #125)

Recoverer comes first, so it wrote the 500 only after the panic had
passed the request log and the metrics, which both recorded 200.
Write500OnPanic, placed after the request log and after the metrics,
writes the 500 as the panic passes and panics again, so Sentry and
Recoverer still get it. Recoverer now writes its 500 only when no
status was written, so the server logs no superfluous WriteHeader call.

Model: opus-5-5

backend/internal/server/routes.go

@@ -34,13 +34,16 @@ func (s *Server) SetupRoutes() {
 	s.router.Use(s.mw.Recoverer())
 	s.router.Use(middleware.RequestID)
 	s.router.Use(s.mw.Logging())
+	// s.mw.Recoverer would write a panic's 500 only after the panic has
+	// passed the request log, so it is written here, where the log sees it.
+	s.router.Use(s.mw.Write500OnPanic())
 	s.router.Use(s.mw.SecurityHeaders())
 	s.router.Use(s.mw.CORS(s.params.Config.CORSAllowedOrigins))
 	s.router.Use(s.mw.MaxBodyBytes(maxRequestBodyBytes))
 	s.router.Use(middleware.Timeout(requestTimeout))
 
-	// Sentry reports a panic, then panics again, so that s.mw.Recoverer
-	// still answers 500.
+	// Sentry reports a panic, then panics again, so that it still
+	// reaches s.mw.Recoverer.
 	if s.params.Config.SentryDSN != "" {
 		s.router.Use(sentryhttp.New(sentryhttp.Options{Repanic: true}).Handle)
 	}
@@ -64,6 +67,8 @@ func (s *Server) SetupRoutes() {
 		// other.
 		if s.params.Config.MetricsUsername != "" {
 			r.Use(s.mw.Metrics(registry))
+			// Likewise inside the metrics.
+			r.Use(s.mw.Write500OnPanic())
 		}
 
 		r.Get("/.well-known/healthcheck", s.h.HandleHealthCheck())