What does Crown of Thorns do in CK3?

Prestige +0.01/month (patch 1.20.0.3).

What if the owner can't benefit from Crown of Thorns?

They get Court grandeur baseline +3 instead.

Court artifact · Pedestal Item

Crown of Thorns

IllustriousUniqueHoly relic

Crown of Thorns is an illustrious pedestal item artifact in Crusader Kings III: Prestige +0.01/month. Quality 100 and wealth 100; maximum durability 150. Patch 1.20.0.3, from game/common/scripted_effects/02_starting_holy_site_relics_effects.txt.

Quick answers (2)

What does Crown of Thorns do in CK3?: Prestige +0.01/month (patch 1.20.0.3).
What if the owner can't benefit from Crown of Thorns?: They get Court grandeur baseline +3 instead.

The crown of thorns pressed upon the head of Christ before the Crucifixion.

Effects

Prestige+0.01/month

For an owner who can't benefit from it

The template gives these instead of the effects above when its “can benefit” check fails:

Court grandeur baseline+3

Who can benefit (can_benefit) (1 line of game script)

christian_artifact_access_trigger = yes

As written in game/common/artifacts/templates (christian_artifact_template).

Counts as a holy relic for (is_holy_relic) (6 lines of game script)

OR = {
	religion = religion:christianity_religion
	main_rite = {
		rite_has_parameter = christian_syncretic_actor
	}
}

As written in game/common/artifacts/templates (christian_artifact_template).

History and who has it

Made before recorded history.

How it is made

Made only inside events; no scripted effect to call from the console.

Source: game/common/scripted_effects/02_starting_holy_site_relics_effects.txt, common/modifiers (artifact_placeholder_modifier), common/artifacts/templates (christian_artifact_template) and the English localisation, Crusader Kings III 1.20.0.3.