Fixes dog fashion items not clearing up when removed from the dog & fixes armor vest dog fashion (#73743)

## About The Pull Request
Restores a `cut_overlays()` to dog's `regenerate_icons()` that was lost
back in #70799.
Also makes an armorvest back fashion for armor vests. When a dog fashion
datum doesn't have `obj_icon_state` declared, it defaults to the
assigned item's icon. Dog fashion's sprite sheet has the armor vest
sprite saved as _armor_. And the only vest that would actually show on a
dog would be an _alt_ armor vest. Apparently, the standard-issue armor
vest uses _armoralt_ icons. Go figure.
However, there are quite a few armor vest subtypes that don't look
anything like the base vest; this needs addressing by either banning
such vests from being used as dog fashion items, or making separate
sprites for them (to be fair, the current dog fashion armor vest needs
an update as well, it's quite old and doesn't correspond to the current
armor vest).
- [x] go around and remove dog fashion from armor vests that don't look
like the base vest

## Why It's Good For The Game
Closes #59224 (hats as items were not stuck, but their sprites were);
dog's sprites will correctly update upon placing/removing a fashion item
Most armor vests placed on a dog will actually show on the sprite

## Changelog
🆑
fix: undressing a hat/back item from a dog will correctly remove the
item's overlay
fix: most armor vests will actually show on a dog when placed on its
back
/🆑

code/datums/dog_fashion.dm

@@ -47,6 +47,13 @@
 /datum/dog_fashion/back
 	icon_file = 'icons/mob/simple/corgi_back.dmi'
 
+/datum/dog_fashion/back/armorvest
+	obj_icon_state = "armor"
+
+/datum/dog_fashion/back/deathsquad
+	name = "Trooper REAL_NAME"
+	desc = "That's not red paint. That's real corgi blood."
+
 /datum/dog_fashion/head/helmet
 	name = "Sergeant REAL_NAME"
 	desc = "The ever-loyal, the ever-vigilant."
@@ -178,10 +185,6 @@
 	speak = list("HONK!", "Honk!")
 	emote_see = list("plays tricks.", "slips.")
 
-/datum/dog_fashion/back/deathsquad
-	name = "Trooper REAL_NAME"
-	desc = "That's not red paint. That's real corgi blood."
-
 /datum/dog_fashion/head/festive
 	name = "Festive REAL_NAME"
 	desc = "Ready to party!"

code/modules/clothing/suits/armor.dm

@@ -34,7 +34,7 @@
 	icon_state = "armoralt"
 	inhand_icon_state = "armor"
 	blood_overlay_type = "armor"
-	dog_fashion = /datum/dog_fashion/back
+	dog_fashion = /datum/dog_fashion/back/armorvest
 
 /obj/item/clothing/suit/armor/vest/alt
 	desc = "A Type I armored vest that provides decent protection against most types of damage."
@@ -100,6 +100,7 @@
 	desc = "A lighter plate armor used to still keep out those pesky arrows, while retaining the ability to move."
 	icon_state = "cuirass"
 	inhand_icon_state = "armor"
+	dog_fashion = null
 
 /obj/item/clothing/suit/armor/hos
 	name = "armored greatcoat"
@@ -453,6 +454,7 @@
 	max_integrity = 200
 	resistance_flags = FLAMMABLE
 	armor_type = /datum/armor/vest_durathread
+	dog_fashion = null
 
 /datum/armor/vest_durathread
 	melee = 20
@@ -469,6 +471,7 @@
 	icon_state = "rus_armor"
 	inhand_icon_state = null
 	armor_type = /datum/armor/vest_russian
+	dog_fashion = null
 
 /datum/armor/vest_russian
 	melee = 25
@@ -488,6 +491,7 @@
 	cold_protection = CHEST|GROIN|LEGS|FEET|ARMS|HANDS
 	min_cold_protection_temperature = SPACE_SUIT_MIN_TEMP_PROTECT
 	armor_type = /datum/armor/vest_russian_coat
+	dog_fashion = null
 
 /datum/armor/vest_russian_coat
 	melee = 25
@@ -556,3 +560,4 @@
 	icon_state = "hop_coat"
 	inhand_icon_state = "b_suit"
 	body_parts_covered = CHEST|GROIN|ARMS
+	dog_fashion = null

code/modules/mob/living/basic/pets/dog.dm

@@ -663,6 +663,7 @@ GLOBAL_LIST_INIT(strippable_corgi_items, create_strippable_list(list(
 
 /mob/living/basic/pet/dog/corgi/regenerate_icons()
 	..()
+	cut_overlays() //we are redrawing the mob after all
 	if(inventory_head)
 		var/image/head_icon
 		var/datum/dog_fashion/DF = new inventory_head.dog_fashion(src)