Fixes bodypart movespeed modifiers (#76520)

## About The Pull Request


![image](https://github.com/tgstation/tgstation/assets/82850673/502a195b-b9d6-48fd-92a1-462e74a13ae0)
I am today's big loser

Fixes https://github.com/tgstation/tgstation/issues/76509 (partly)
This was caused by my goofy ass not using the correct proc for the
VARIABLE movespeed modifier that is the bodypart one.

Additionally slightly changes some bodypart code that bothered me by
using signals even though it was just... not really necessary? And kind
of confusing?

## Why It's Good For The Game

Bugs are bad they make you mad

## Changelog

🆑
fix: Bodyparts that should slow you down, will slow you down.
/🆑

code/modules/surgery/bodyparts/_bodyparts.dm

@@ -649,6 +649,15 @@
 	SEND_SIGNAL(src, COMSIG_BODYPART_CHANGED_OWNER, new_owner, old_owner)
 	var/needs_update_disabled = FALSE //Only really relevant if there's an owner
 	if(old_owner)
+		if(held_index)
+			old_owner.on_lost_hand(src)
+			if(old_owner.hud_used)
+				var/atom/movable/screen/inventory/hand/hand = old_owner.hud_used.hand_slots["[held_index]"]
+				if(hand)
+					hand.update_appearance()
+			old_owner.update_worn_gloves()
+		if(speed_modifier)
+			old_owner.update_bodypart_speed_modifier()
 		if(length(bodypart_traits))
 			old_owner.remove_traits(bodypart_traits, bodypart_trait_source)
 		if(initial(can_be_disabled))
@@ -664,6 +673,15 @@
 				))
 		UnregisterSignal(old_owner, COMSIG_ATOM_RESTYLE)
 	if(owner)
+		if(held_index)
+			owner.on_added_hand(src, held_index)
+			if(owner.hud_used)
+				var/atom/movable/screen/inventory/hand/hand = owner.hud_used.hand_slots["[held_index]"]
+				if(hand)
+					hand.update_appearance()
+			owner.update_worn_gloves()
+		if(speed_modifier)
+			owner.update_bodypart_speed_modifier()
 		if(length(bodypart_traits))
 			owner.add_traits(bodypart_traits, bodypart_trait_source)
 		if(initial(can_be_disabled))

code/modules/surgery/bodyparts/dismemberment.dm

@@ -92,11 +92,8 @@
 	SEND_SIGNAL(owner, COMSIG_CARBON_REMOVE_LIMB, src, dismembered)
 	SEND_SIGNAL(src, COMSIG_BODYPART_REMOVED, owner, dismembered)
 	update_limb(dropping_limb = TRUE)
-	//limb is out and about, it can't really be considered an implant
-	bodypart_flags &= ~BODYPART_IMPLANTED
+	bodypart_flags &= ~BODYPART_IMPLANTED //limb is out and about, it can't really be considered an implant
 	owner.remove_bodypart(src)
-	if(speed_modifier)
-		owner.update_bodypart_speed_modifier()
 
 	for(var/datum/wound/wound as anything in wounds)
 		wound.remove_wound(TRUE)
@@ -125,7 +122,7 @@
 	if(!special)
 		if(phantom_owner.dna)
 			for(var/datum/mutation/human/mutation as anything in phantom_owner.dna.mutations) //some mutations require having specific limbs to be kept.
-				if(mutation.limb_req && mutation.limb_req == body_zone)
+				if(mutation.limb_req && (mutation.limb_req == body_zone))
 					to_chat(phantom_owner, span_warning("You feel your [mutation] deactivating from the loss of your [body_zone]!"))
 					phantom_owner.dna.force_lose(mutation)
 
@@ -331,15 +328,6 @@
 	moveToNullspace()
 	set_owner(new_limb_owner)
 	new_limb_owner.add_bodypart(src)
-	if(held_index)
-		new_limb_owner.on_added_hand(src, held_index)
-		if(new_limb_owner.hud_used)
-			var/atom/movable/screen/inventory/hand/hand = new_limb_owner.hud_used.hand_slots["[held_index]"]
-			if(hand)
-				hand.update_appearance()
-		new_limb_owner.update_worn_gloves()
-	if(speed_modifier)
-		new_limb_owner.update_bodypart_speed_modifier()
 
 	if(special) //non conventional limb attachment
 		for(var/datum/surgery/attach_surgery as anything in new_limb_owner.surgeries) //if we had an ongoing surgery to attach a new limb, we stop it.