What do you get for winning a Sovereignty War war in CK3?

The attacker gains the contested tributaries (patch 1.20.0.3).

What does the Sovereignty War casus belli cost?

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

Casus belli · Subjugation

Sovereignty War

The war is called “Sovereignty War”

Sovereignty War is a casus belli in Crusader Kings III (subjugation). If the attacker wins: The attacker gains the contested tributaries. If the defender wins: The defender keeps the contested tributaries, and the attacker must pay them war reparations. Declaring it costs prestige. The war goal is worth 80% war score. 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 Sovereignty War war in CK3?: The attacker gains the contested tributaries (patch 1.20.0.3).
What happens on a white peace?: The defender keeps the contested tributaries.
What does the Sovereignty War casus belli cost?: prestige; the amount depends on the titles, claims and distance, worked out when you declare.

How the war ends

Attacker wins

The attacker gains the contested tributaries.

White peace

The defender keeps the contested tributaries.

Defender wins

The defender keeps the contested tributaries, and the attacker must pay them war reparations.

If the war becomes invalid

They do not border your Realm or that of your Tributaries

Who can declare it

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

Every subjugation war (the group's allowed_for_character) (13 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
OR = {
	NOT = {
		government_has_flag = government_is_theocracy
	}
	AND = {
		government_has_flag = government_is_theocracy
		has_variable = koh_subjugation_cb_allowed
	}
}

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

Attacker (allowed_for_character) (10 lines of game script)

scope:attacker = {
	is_landed = yes
	trigger_if = {
		limit = {
			is_ai = yes
		}
		highest_held_title_tier >= tier_kingdom
	}
	government_has_flag = government_is_nomadic
}

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

Defender (allowed_against_character) (12 lines of game script)

scope:defender = {
	is_landed = yes
	government_has_flag = government_is_nomadic
}
NOR = {
	scope:defender = {
		target_is_liege_or_above = scope:attacker
	}
	scope:attacker = {
		target_is_liege_or_above = scope:defender
	}
}

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

When it can start (valid_to_start) (10 lines of game script)

scope:defender = {
	any_tributary = {
		any_neighboring_top_liege_realm_owner = {
			OR = {
				this = scope:attacker
				suzerain ?= scope:attacker
			}
		}
	}
}

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

Cost to declare

Costs 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 (4 lines of game script)

prestige = {
	value = 250
	multiply = common_cb_prestige_cost_multiplier
}

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.