What do you get for winning a Sōryō Conquest war in CK3?

The attacker gains the contested Title (patch 1.20.0.3).

What does the Sōryō Conquest casus belli cost?

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

Casus belli · Conquest

Sōryō Conquest

All Under Heaven

Sōryō Conquest is a casus belli in Crusader Kings III (conquest). If the attacker wins: The attacker gains the contested Title. If the defender wins: The defender keeps the contested Title. Declaring it costs prestige. The war goal is worth 1% war score. It needs All Under Heaven. Patch 1.20.0.3, from game/common/casus_belli_types/10_tgp_japan_wars.txt.

Quick answers (3)

What do you get for winning a Sōryō Conquest war in CK3?: The attacker gains the contested Title (patch 1.20.0.3).
What happens on a white peace?: The defender keeps the contested Title.
What does the Sōryō Conquest 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 Title.

White peace

The defender keeps the contested Title.

Defender wins

The defender keeps the contested Title.

If the war becomes invalid

Sōryō Conquest was invalidated

Who can declare it

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

Every conquest 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) (3 lines of game script)

has_tgp_dlc_trigger = yes
is_landed = yes
tgp_soryo_or_bushido_trigger = yes

As written in game/common/casus_belli_types/10_tgp_japan_wars.txt.

Defender (allowed_against_character) (6 lines of game script)

top_liege ?= {
	this = scope:attacker.top_liege
	NOT = {
		this = scope:attacker
	}
}

As written in game/common/casus_belli_types/10_tgp_japan_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 (7 lines of game script)

prestige = {
	add = {
		value = 100
		desc = CB_BASE_COST
	}
	multiply = common_cb_prestige_cost_multiplier
}

As written in game/common/casus_belli_types/10_tgp_japan_wars.txt.

Source: game/common/casus_belli_types/10_tgp_japan_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.