Refactors fire overlays once again to make it not get stuck so often (#81367)

## About The Pull Request

Maybe finally fixes #77701 

A big reason why this kept happening is because fire uses standing
overlays. But fire isn't managed by mobs anymore. Meaning in some
situations, fire can cease to exist but the overlay can still be on the
mob. So it gets stuck.

So like, why use standing overlays anymore? We can just hook
`update_overlays` signal.
Isn't that neat. 

## Changelog

🆑 Melbert
refactor: Fire effects get added to mobs in a different way now. Maybe
it will get stuck less. Report any oddities.
/🆑

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

@@ -270,17 +270,17 @@
 /mob/living/basic/on_fire_stack(seconds_per_tick, datum/status_effect/fire_handler/fire_stacks/fire_handler)
 	adjust_bodytemperature((maximum_survivable_temperature + (fire_handler.stacks * 12)) * 0.5 * seconds_per_tick)
 
-/mob/living/basic/update_fire_overlay(stacks, on_fire, last_icon_state, suffix = "")
-	var/mutable_appearance/fire_overlay = mutable_appearance('icons/mob/effects/onfire.dmi', "generic_fire")
-	if(on_fire && isnull(last_icon_state))
-		add_overlay(fire_overlay)
-		return fire_overlay
-	else if(!on_fire && !isnull(last_icon_state))
-		cut_overlay(fire_overlay)
-		return null
-	else if(on_fire && !isnull(last_icon_state))
-		return last_icon_state
-	return null
+/mob/living/basic/get_fire_overlay(stacks, on_fire)
+	var/fire_icon = "generic_fire"
+	if(!GLOB.fire_appearances[fire_icon])
+		GLOB.fire_appearances[fire_icon] = mutable_appearance(
+			'icons/mob/effects/onfire.dmi',
+			fire_icon,
+			-HIGHEST_LAYER,
+			appearance_flags = RESET_COLOR,
+		)
+
+	return GLOB.fire_appearances[fire_icon]
 
 /mob/living/basic/put_in_hands(obj/item/I, del_on_fail = FALSE, merge_stacks = TRUE, ignore_animation = TRUE)
 	. = ..()