Game concept · All Under Heaven
Ceremonial Monarch
The game also links it as Ceremonial Monarch's.
From the game's encyclopedia
In certain Realms (such as Japan) a powerful bureaucrat or commander may have taken true power as a Ruling Regent, leaving a nominally reigning Ceremonial Monarch as a mere figurehead and Vassal in practice. All members of a Ceremonial Monarch's House are considered part of the Ceremonial House.
Despite not ruling directly, the Ceremonial House is the most esteemed bloodline in a realm, and other Houses will gain more Prestige for marriages with them, with such connections strongly influencing the succession of the Ruling Regent.
The Ceremonial Monarch may take back true power if they somehow regain the Primary Title of the realm, such as by Faction demand or competing for the Ruling Regent Title using Influence.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Ceremonial Monarch is an entry of Crusader Kings III's in-game encyclopedia (All Under Heaven). The game explains it: "In certain Realms (such as Japan) a powerful bureaucrat or commander may have taken true power as a Ruling Regent, leaving a nominally reigning Ceremonial Monarch as a mere figurehead and Vassal in practice." It covers Ceremonial House and Japanese Emperor. The game also links it as Ceremonial Monarch's. Patch 1.20.1.2, from game/common/game_concepts/tgp_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/tgp_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.