What does the Greatest of Khans' Onslaught casus belli cost?

piety and prestige; the amount depends on the titles, claims and distance, worked out when you declare.

Casus belli · Invasions

Greatest of Khans' Onslaught

Khans of the Steppe

Greatest of Khans' Onslaught is a casus belli in Crusader Kings III (invasions). If the attacker wins: The attacker takes all of the defender's lands, as well as titles belonging to them and their stronger vassals. If the defender wins: … remains an independent ruler, losing only occupied counties. The attacker is humiliated. Declaring it costs piety and prestige. The war goal is worth 80% war score. It needs Khans of the Steppe. Patch 1.20.0.3, from game/common/casus_belli_types/09_mpo_wars.txt.

Quick answers (3)

What do you get for winning a Greatest of Khans' Onslaught war in CK3?: The attacker takes all of the defender's lands, as well as titles belonging to them and their stronger vassals (patch 1.20.0.3).
What happens on a white peace?: The defender remains an independent ruler, losing only occupied counties.
What does the Greatest of Khans' Onslaught casus belli cost?: piety and prestige; the amount depends on the titles, claims and distance, worked out when you declare.

How the war ends

Attacker wins

The attacker takes all of the defender's lands, as well as titles belonging to them and their stronger vassals.

White peace

The defender remains an independent ruler, losing only occupied counties.

Defender wins

… remains an independent ruler, losing only occupied counties. The attacker is humiliated.

If the war becomes invalid

The … has ended: the defender can no longer be subjugated.

Who can declare it

The game shows no text of its own for these conditions; the script is below.

Every invasions war (the group's allowed_for_character) (7 lines of game script)

herders_and_tributary_constraints = yes
pam_personal_pacifism_offensive_war_ban_trigger = yes
tgp_dynastic_cycle_offensive_wars_ban_trigger = yes
tgp_war_ban_all_ministers_trigger = yes
NOT = {
	government_has_flag = government_is_theocracy
}

As written in game/common/casus_belli_groups/00_casus_belli_groups.txt.

Attacker (allowed_for_character) (7 lines of game script)

any_owned_story = {
	OR = {
		story_type = story_greatest_of_khans
		story_type = story_mongol_invasion
	}
}
has_mpo_dlc_trigger = yes

As written in game/common/casus_belli_types/09_mpo_wars.txt.

Defender (allowed_against_character) (6 lines of game script)

scope:attacker = {
	ALL_FALSE = {
		top_liege = scope:defender.top_liege
		liege = scope:defender
	}
}

As written in game/common/casus_belli_types/09_mpo_wars.txt.

Cost to declare

Costs piety and prestige. The amount is worked out when you declare (by the titles targeted, claims, distance and more), so the script is shown as written:

Cost (46 lines of game script)

piety = {
	value = 0
	if = {
		limit = {
			scope:attacker.faith.religious_head ?= scope:attacker
			scope:defender.faith = scope:attacker.faith
		}
		add = {
			value = 500
			desc = CB_BASE_COST
		}
	}
	if = {
		limit = {
			scope:attacker = {
				is_ai = yes
			}
		}
		multiply = 0
	}
	add = common_cb_impious_piety_cost
	multiply = common_cb_piety_cost_multiplier
}
prestige = {
	add = {
		value = 500
		desc = CB_BASE_COST
	}
	multiply = common_cb_prestige_cost_multiplier
	if = {
		limit = {
			scope:attacker = {
				has_character_flag = is_temujin
			}
		}
		multiply = 0
	}
	if = {
		limit = {
			scope:attacker = {
				is_ai = yes
			}
		}
		multiply = 0
	}
}

As written in game/common/casus_belli_types/09_mpo_wars.txt.

Source: game/common/casus_belli_types/09_mpo_wars.txt and the English localisation, Crusader Kings III 1.20.0.3. “The attacker”, “the defender” stand where the game names the character; “…” marks other words it fills in during play.