fix: API JSON error responses + navbar with dropdowns

- Add backend/libs/go-http-errors for consistent JSON errors
- REST API: use writeMethodNotAllowed, writeNotFound, writeInternalError
- middleware, gateway, search: use httperrors.WriteJSON
- SPA: navbar with Explore/Tools/More dropdowns, initNavDropdowns()
- Next.js: Navbar component with dropdowns + mobile menu

Co-authored-by: Cursor <cursoragent@cursor.com>

backend/libs/go-http-errors/errors.go

@@ -0,0 +1,26 @@
+package httperrors
+
+import (
+	"encoding/json"
+	"net/http"
+)
+
+// ErrorResponse is the standard JSON error body for API responses.
+type ErrorResponse struct {
+	Error struct {
+		Code    string `json:"code"`
+		Message string `json:"message"`
+	} `json:"error"`
+}
+
+// WriteJSON writes a JSON error response with the given status code and message.
+func WriteJSON(w http.ResponseWriter, statusCode int, code, message string) {
+	w.Header().Set("Content-Type", "application/json")
+	w.WriteHeader(statusCode)
+	json.NewEncoder(w).Encode(ErrorResponse{
+		Error: struct {
+			Code    string `json:"code"`
+			Message string `json:"message"`
+		}{Code: code, Message: message},
+	})
+}