Test the 503 for a request waiting on a transcode stopped at a deadline

A request that waited for another request's transcode, stopped at that
request's deadline, must get ErrProcessingTimedOut, which both image
routes answer 503. Declares that error so the tests build. Also tests
that Process, past its deadline before it starts, never reads its input.

Model: opus-5-5

internal/handlers/server_busy_internal_test.go

@@ -1,6 +1,7 @@
 package handlers
 
 import (
+	"context"
 	"fmt"
 	"log/slog"
 	"net/http"
@@ -47,3 +48,40 @@ func TestServerBusyAnswers503(t *testing.T) {
 		}
 	}
 }
+
+// TestProcessingTimedOutAnswers503 checks that respondImageError and
+// handleImageError, which answer the errors of the two image routes, answer
+// 503 with the server busy error when the image service reports that
+// processing stopped at the deadline of the request doing it, wrapped as the
+// service wraps it. A request that waited for that processing gets this error
+// while its own deadline may have time left. The request's source only goes
+// into a log line, so it is left empty.
+func TestProcessingTimedOutAnswers503(t *testing.T) {
+	t.Parallel()
+
+	h := &Handlers{log: slog.New(slog.DiscardHandler)}
+	err := fmt.Errorf("%w: failed to encode: %w",
+		imgcache.ErrProcessingTimedOut, context.DeadlineExceeded)
+
+	plain := httptest.NewRecorder()
+	h.respondImageError(plain, &imgcache.ImageRequest{}, err)
+
+	encrypted := httptest.NewRecorder()
+	h.handleImageError(encrypted, err)
+
+	for name, rec := range map[string]*httptest.ResponseRecorder{
+		"respondImageError": plain, "handleImageError": encrypted,
+	} {
+		t.Logf("%s: status = %d, body = %q", name, rec.Code, rec.Body.String())
+
+		if rec.Code != http.StatusServiceUnavailable {
+			t.Errorf("%s: status = %d, want %d",
+				name, rec.Code, http.StatusServiceUnavailable)
+		}
+
+		if !strings.Contains(rec.Body.String(), "server busy, try again later") {
+			t.Errorf("%s: body = %q, want the server busy error",
+				name, rec.Body.String())
+		}
+	}
+}