Fix LEVEL_CORNERS_USE_PROBE with BLTOUCH_HS_MODE (#21161)

Marlin/src/lcd/menu/menu_bed_corners.cpp

     do {
       ui.refresh(LCDVIEW_REDRAW_NOW);
       _lcd_draw_probing();                                             // update screen with # of good points
-      do_blocking_move_to_z(current_position.z + LEVEL_CORNERS_Z_HOP); // clearance
+      do_blocking_move_to_z(current_position.z + LEVEL_CORNERS_Z_HOP + TERN0(BLTOUCH_HS_MODE, 7)); // clearance
 
       _lcd_level_bed_corners_get_next_position();         // Select next corner coordinates
       current_position -= probe.offset_xy;                // Account for probe offsets
       do_blocking_move_to_xy(current_position);           // Goto corner
 
+      TERN_(BLTOUCH_HS_MODE, bltouch.deploy());           // Deploy in HIGH SPEED MODE
       if (!_lcd_level_bed_corners_probe()) {              // Probe down to tolerance
         if (_lcd_level_bed_corners_raise()) {             // Prompt user to raise bed if needed
           #if ENABLED(LEVEL_CORNERS_VERIFY_RAISED)        // Verify
 
     } while (good_points < nr_edge_points); // loop until all points within tolerance
 
+    TERN_(BLTOUCH_HS_MODE, do_blocking_move_to_z(current_position.z + LEVEL_CORNERS_Z_HOP)); // Do clearance in HIGH SPEED MODE at the very end
+    TERN_(BLTOUCH_HS_MODE, bltouch.stow()); // Stow in HIGH SPEED MODE at the very end
+
     ui.goto_screen(_lcd_draw_level_prompt); // prompt for bed leveling
     ui.set_selection(true);
   }