From the game's encyclopedia
A Diarch's Loyalty decides how likely it is they will abuse their powers, at their Liege's or the Realm's expense.
Selfless Diarchs refrain from using Borrowed Powers, try to fulfil the Mandate set for them dutifully, and give up their power willingly when asked.
Self-Interested Diarchs use Borrowed Powers liberally, try to fulfil their Mandate in order to swing the Scales of Power in their direction, and may refuse to give up power if the Scales are swung heavily enough towards them.
Situational Diarchs might use Borrowed Powers, will generally either split Mandate benefits with their Liege or ignore their Mandate entirely, and might need bribing to give up their office if the Scales of Power suit them.
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.
Loyalty is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Diarch's Loyalty decides how likely it is they will abuse their powers, at their Liege's or the Realm's expense." It is part of Power Sharing. The game also links it as Diarch Loyalty and Loyal. Patch 1.20.1.2, from game/common/game_concepts/04_ep2_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/04_ep2_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.