feat(gui): multi-nozzle UI for H2C/A2L

Multi-nozzle sync widget, AMS rack-nozzle mapping popup, calibration rework, send-dialog nozzle mapping and extruder-count UI. Includes the fix to persist the AMS sync badge on filament cards (H2C/A2L and direct-sync printers).

src/slic3r/GUI/Plater.hpp

@@ -50,6 +50,7 @@ class SLAPrint;
 //BBS: add partplatelist and SlicingStatusEvent
 class PartPlateList;
 class SlicingStatusEvent;
+class BackgroundSlicingProcess;
 enum SLAPrintObjectStep : unsigned int;
 enum class ConversionType : int;
 class DevAms;
@@ -519,6 +520,9 @@ public:
     void schedule_background_process(bool schedule = true);
     bool is_background_process_update_scheduled() const;
     void suppress_background_process(const bool stop_background_process) ;
+    // Expose the slicing process so the device GUI can read the current
+    // GCodeProcessorResult (e.g. the nozzle grouping for print-dispatch mapping).
+    BackgroundSlicingProcess& background_process();
     /* -1: send current gcode if not specified
      * -2: send all gcode to target machine */
     int send_gcode(int plate_idx = -1, Export3mfProgressFn proFn = nullptr);