Fixes external_bodyshapes not always applying its bodyshape to owner (#92698)

## About The Pull Request

The synchronize procs ran too early and would miss out on the last organ
loaded, which is more likely to happen than you think.

## Why It's Good For The Game

In case TG ever wants to code mask sprites for snouted humanoids, you'll
want this to work.

code/modules/surgery/organs/organ_movement.dm

@@ -74,11 +74,6 @@
 		wash(CLEAN_TYPE_BLOOD)
 		organ_flags &= ~ORGAN_VIRGIN
 
-	if(external_bodytypes)
-		receiver.synchronize_bodytypes()
-	if(external_bodyshapes)
-		receiver.synchronize_bodyshapes()
-
 	receiver.organs |= src
 	receiver.organs_slot[slot] = src
 	owner = receiver
@@ -141,6 +136,11 @@
 	ADD_TRAIT(src, TRAIT_NODROP, ORGAN_INSIDE_BODY_TRAIT)
 	interaction_flags_item &= ~INTERACT_ITEM_ATTACK_HAND_PICKUP
 
+	if(external_bodytypes)
+		limb.owner?.synchronize_bodytypes()
+	if(external_bodyshapes)
+		limb.owner?.synchronize_bodyshapes()
+
 	if(bodypart_overlay)
 		limb.add_bodypart_overlay(bodypart_overlay)
 
@@ -186,8 +186,6 @@
 	SEND_SIGNAL(organ_owner, COMSIG_CARBON_LOSE_ORGAN, src, special)
 	ADD_TRAIT(src, TRAIT_USED_ORGAN, ORGAN_TRAIT)
 
-	organ_owner.synchronize_bodytypes()
-	organ_owner.synchronize_bodyshapes()
 	if(!special)
 		organ_owner.hud_used?.update_locked_slots()
 
@@ -248,6 +246,9 @@
 	REMOVE_TRAIT(src, TRAIT_NODROP, ORGAN_INSIDE_BODY_TRAIT)
 	interaction_flags_item |= INTERACT_ITEM_ATTACK_HAND_PICKUP
 
+	limb.owner?.synchronize_bodytypes()
+	limb.owner?.synchronize_bodyshapes()
+
 	if(!bodypart_overlay)
 		return