Record an exception as an error only when Plug.Exception.status/1

returns 500..599.

It is encouraged in the Phoenix docs to use `Plug.Exception` with
custom exceptions to generate for example 404 responses at certain
places. These 404s should not be marked as error, since simple "route
not found" 404s are also not marked as error.

instrumentation/opentelemetry_phoenix/lib/opentelemetry_phoenix.ex

@@ -224,9 +224,15 @@ defmodule OpentelemetryPhoenix do
       # try to normalize all errors to Elixir exceptions
       exception = Exception.normalize(kind, reason, stacktrace)
 
-      # record exception and mark the span as errored
-      Tracer.record_exception(exception, stacktrace, attrs)
-      Tracer.set_status(OpenTelemetry.status(:error, ""))
+      case Plug.Exception.status(exception) do
+        500..599 ->
+          # record exception and mark the span as errored
+          Tracer.record_exception(exception, stacktrace, attrs)
+          Tracer.set_status(OpenTelemetry.status(:error, ""))
+
+        _ ->
+          nil
+      end
 
       # do not close the span as endpoint stop will still be called with
       # more info, including the status code, which is nil at this stage