Minor cleanup of pause code (#13030)

Marlin/src/feature/pause.cpp

@@ -329,12 +329,6 @@ bool pause_print(const float &retract, const point_t &park_point, const float &u
     host_action_pause();
   #endif
 
-  #if HAS_LCD_MENU
-    if (show_lcd) lcd_advanced_pause_show_message(ADVANCED_PAUSE_MESSAGE_INIT, ADVANCED_PAUSE_MODE_PAUSE_PRINT);
-  #else
-    UNUSED(show_lcd);
-  #endif
-
   if (!DEBUGGING(DRYRUN) && unload_length && thermalManager.targetTooColdToExtrude(active_extruder)) {
     SERIAL_ECHO_MSG(MSG_ERR_HOTEND_TOO_COLD);
 
@@ -343,6 +337,8 @@ bool pause_print(const float &retract, const point_t &park_point, const float &u
         lcd_advanced_pause_show_message(ADVANCED_PAUSE_MESSAGE_STATUS);
         LCD_MESSAGEPGM(MSG_M600_TOO_COLD);
       }
+    #else
+      UNUSED(show_lcd);
     #endif
 
     return false; // unable to reach safe temperature

Marlin/src/gcode/feature/pause/M125.cpp

@@ -79,8 +79,8 @@ void GcodeSuite::M125() {
   #endif
 
   #if HAS_LCD_MENU
+    lcd_advanced_pause_show_message(ADVANCED_PAUSE_MESSAGE_INIT, ADVANCED_PAUSE_MODE_PAUSE_PRINT);
     const bool show_lcd = parser.seenval('P');
-    lcd_advanced_pause_show_message(ADVANCED_PAUSE_MESSAGE_INIT, ADVANCED_PAUSE_MODE_PAUSE_PRINT, active_extruder);
   #else
     constexpr bool show_lcd = false;
   #endif

Marlin/src/lcd/menu/menu_main.cpp

@@ -48,8 +48,8 @@ void lcd_pause() {
   #endif
 
   #if ENABLED(PARK_HEAD_ON_PAUSE)
-    lcd_advanced_pause_show_message(ADVANCED_PAUSE_MESSAGE_INIT, ADVANCED_PAUSE_MODE_PAUSE_PRINT, active_extruder);
-    enqueue_and_echo_commands_P(PSTR("M25 P; \n M24"));
+    lcd_advanced_pause_show_message(ADVANCED_PAUSE_MESSAGE_INIT, ADVANCED_PAUSE_MODE_PAUSE_PRINT);  // Show message immediately to let user know about pause in progress
+    enqueue_and_echo_commands_P(PSTR("M25 P\nM24"));
   #elif ENABLED(SDSUPPORT)
     enqueue_and_echo_commands_P(PSTR("M25"));
   #elif defined(ACTION_ON_PAUSE)