Pixel adjustments to mobs are now sourced / Refactors riding (#89320)

Fixes #85980

- Pixel adjustments are now sourced

When tweaking a mob's pixel w, x, y, z, is is now done via `add_offsets`
and must have a source string associated

- Refactors riding

Refactors how riding component selects the offsets to use. It's now all
done via the getter rather than a weird mix of a var, a cache, and a
getter.

- Moves a bunch of animations to use `pixel_w` / `pixel_z`

Largely to prevent conflicts with adjustments to a mob's pixel position,
but also as many animations are not actual movements, but visual
movements. Floating is one such example.

It just works

🆑 Melbert
fix: Fixed grab offsets not showing for anything but passive grab
fix: Fix jank with mob offsets when riding things
refactor: Refactored riding component, particularly how it selects layer
and offsets. Report any oddities
refactor: Refactored pixel offsets of mobs. Report any oddities
/🆑

code/modules/mob/living/basic/pets/parrot/_parrot.dm

@@ -104,6 +104,7 @@ GLOBAL_LIST_INIT(strippable_parrot_items, create_strippable_list(list(
 	RegisterSignal(src, COMSIG_ATOM_WAS_ATTACKED, PROC_REF(on_injured)) // this means we got hurt and it's go time
 	RegisterSignal(src, COMSIG_ANIMAL_PET, PROC_REF(on_pet))
 	RegisterSignal(src, COMSIG_KB_MOB_DROPITEM_DOWN, PROC_REF(drop_item_on_signal))
+	ADD_TRAIT(src, TRAIT_CAN_MOUNT_HUMANS, INNATE_TRAIT)
 
 /mob/living/basic/parrot/Destroy()
 	// should have cleaned these up on death, but let's be super safe in case that didn't happen
@@ -264,13 +265,19 @@ GLOBAL_LIST_INIT(strippable_parrot_items, create_strippable_list(list(
 	UnregisterSignal(src, COMSIG_LIVING_SET_BUCKLED)
 	toggle_perched(perched = FALSE)
 
+#define PERCH_SOURCE "perched"
+
 /mob/living/basic/parrot/proc/toggle_perched(perched)
 	if(!perched)
-		REMOVE_TRAIT(src, TRAIT_PARROT_PERCHED, TRAIT_GENERIC)
+		REMOVE_TRAIT(src, TRAIT_PARROT_PERCHED, PERCH_SOURCE)
+		remove_offsets(PERCH_SOURCE)
 	else
-		ADD_TRAIT(src, TRAIT_PARROT_PERCHED, TRAIT_GENERIC)
+		ADD_TRAIT(src, TRAIT_PARROT_PERCHED, PERCH_SOURCE)
+		add_offsets(PERCH_SOURCE, y_add = 9)
 	update_appearance(UPDATE_ICON_STATE)
 
+#undef PERCH_SOURCE
+
 /// Master proc which will determine the intent of OUR attacks on an object and summon the relevant procs accordingly.
 /// This is pretty much meant for players, AI will use the task-specific procs instead.
 /mob/living/basic/parrot/early_melee_attack(atom/target, list/modifiers, ignore_cooldown)