fix: chat build syntax errors, disable GitHub cache on Gitea runner

- Fix 3 orphaned function bodies in main.go (handleAdminSchedule,
  handleAdminSystemSummary, probeMediaDurationSeconds) caused by
  insertions that split function headers from bodies
- Remove cache: true from setup-go and cache: npm from setup-node
  (Gitea runner times out 135s trying to reach GitHub cache API)
- Add go vet ./... step replacing placeholder echo
- Remove || echo fallback from lint (tsc --noEmit is working)

backend/chat/src/main.go

@@ -767,6 +767,8 @@ func handleAdminScheduleOverrides(w http.ResponseWriter, r *http.Request) {
 		http.Error(w, "method not allowed", http.StatusMethodNotAllowed)
 	}
 }
+
+func handleAdminSchedule(w http.ResponseWriter, r *http.Request) {
 	if r.Method != http.MethodGet {
 		http.Error(w, "method not allowed", http.StatusMethodNotAllowed)
 		return
@@ -1062,14 +1064,9 @@ func handleAdminRestart(w http.ResponseWriter, r *http.Request) {
 		"message": fmt.Sprintf("Restart %s manually: docker compose -f docker-compose.prod.yml restart %s", service, service),
 	})
 }
-	if r.Method != http.MethodGet {
-		http.Error(w, "method not allowed", http.StatusMethodNotAllowed)
-		return
-	}
 
-	w.Header().Set("Content-Type", "application/json")
-	json.NewEncoder(w).Encode(getAdminSystemSummary())
-}
+func handleAdminSystemSummary(w http.ResponseWriter, r *http.Request) {
+	if r.Method != http.MethodGet {
 
 func handleAdminUsers(w http.ResponseWriter, r *http.Request) {
 	switch r.Method {
@@ -1445,6 +1442,7 @@ func validateMediaNormalization(mediaPath string) MediaNormalizationResult {
 
 	return result
 }
+func probeMediaDurationSeconds(mediaPath string) (int, error) {
 	ctx, cancel := context.WithTimeout(context.Background(), 20*time.Second)
 	defer cancel()